Datasets:
christopher
/
oeis

Dataset card Data Studio Files
xet
Community
2
sequence_id
stringlengths
7
7
sequence_name
stringlengths
4
573
sequence
listlengths
1
348
keywords
listlengths
1
8
score
int64
1
2.35k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
⌀
cross_references
listlengths
1
128
⌀
former_ids
listlengths
1
3
⌀
author
stringlengths
7
231
⌀
timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-07-19 00:40:46
filename
stringlengths
29
29
hash
stringlengths
32
32
A015101
Inverse of 1092nd cyclotomic polynomial.
[ "1", "0", "1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "1", "0", "1", "0", "-1", "0", "-1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "-1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "-1", "0", "-1", "0", "1", "0", "1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0" ]
[ "sign" ]
16
0
1
null
null
Simon Plouffe
2023-03-05T11:26:50
oeisdata/seq/A015/A015101.seq
c7207ba13b383eeac51209d0824a3aad
A015102
Carlitz-Riordan q-Catalan numbers (recurrence version) for q=-6.
[ "1", "1", "-5", "-191", "40915", "53110057", "-412878084725", "-19264066381851695", "5392667163887921078275", "9057620836725683164283293369", "-91279931160615494871228103624209605" ]
[ "sign" ]
37
0
3
[ "A000108", "A015083", "A015084", "A015085", "A015086", "A015089", "A015091", "A015092", "A015093", "A015095", "A015096", "A015097", "A015098", "A015099", "A015100", "A015102", "A015103", "A015105", "A015106", "A015107", "A015108", "A090192", "A227543", "A290789" ]
null
Olivier Gérard
2019-11-17T09:30:14
oeisdata/seq/A015/A015102.seq
1404c181cfeb594454b3619b1aa45e58
A015103
Carlitz-Riordan q-Catalan numbers (recurrence version) for q=-7.
[ "1", "1", "-6", "-307", "104742", "251699498", "-4229811552588", "-497641562809372379", "409828230340907182689774", "2362579011761419853955236859806", "-95338580221916838164306067991935130836" ]
[ "sign" ]
36
0
3
[ "A000108", "A015083", "A015084", "A015085", "A015086", "A015089", "A015091", "A015092", "A015093", "A015095", "A015096", "A015097", "A015098", "A015099", "A015100", "A015102", "A015103", "A015105", "A015106", "A015107", "A015108", "A090192", "A227543", "A290789" ]
null
Olivier Gérard
2024-08-04T16:30:44
oeisdata/seq/A015/A015103.seq
8d630c1e99da17b3e625d42f9896d6a2
A015104
Inverse of 1095th cyclotomic polynomial.
[ "1", "-1", "0", "1", "-1", "1", "0", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "0", "1", "-1", "1", "0", "-1" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2023-04-30T12:29:37
oeisdata/seq/A015/A015104.seq
96483cf2d8980ca064107bfa4ace90f0
A015105
Carlitz-Riordan q-Catalan numbers (recurrence version) for q=-8.
[ "1", "1", "-7", "-463", "236201", "967959393", "-31716161292711", "-8314264834902720111", "17436260499054618815283977", "292531943497569504642889779448001", "-39262972238604561849241166988994502971207" ]
[ "sign" ]
31
0
3
[ "A000108", "A015083", "A015084", "A015085", "A015086", "A015089", "A015091", "A015092", "A015093", "A015095", "A015096", "A015097", "A015098", "A015099", "A015100", "A015102", "A015103", "A015105", "A015106", "A015107", "A015108", "A090192", "A227543", "A290789" ]
null
Olivier Gérard
2019-11-17T09:30:26
oeisdata/seq/A015/A015105.seq
870a7d26082c9f96d58456ec8b04fdad
A015106
Carlitz-Riordan q-Catalan numbers (recurrence version) for q=-9.
[ "1", "1", "-8", "-665", "483544", "3173511682", "-187386353065808", "-99585165693268026701", "476312561203989614441440600", "20503694883570579788445502041773422", "-7943551457092331370323478258038812629918704" ]
[ "sign" ]
30
0
3
[ "A000108", "A015083", "A015084", "A015085", "A015086", "A015089", "A015091", "A015092", "A015093", "A015095", "A015096", "A015097", "A015098", "A015099", "A015100", "A015102", "A015103", "A015105", "A015106", "A015107", "A015108", "A090192", "A227543", "A290789" ]
null
Olivier Gérard
2019-11-17T09:30:32
oeisdata/seq/A015/A015106.seq
1d8f032fe1593536a90eb39a0afb0112
A015107
Carlitz-Riordan q-Catalan numbers (recurrence version) for q=-10.
[ "1", "1", "-9", "-919", "917271", "9174563561", "-917438025443049", "-917439860513400673559", "9174396770273536422744011031", "917439695376166450708460281823359721", "-917439693541287252616828116888122637934368489" ]
[ "sign" ]
30
0
3
[ "A000108", "A015083", "A015084", "A015085", "A015086", "A015089", "A015091", "A015092", "A015093", "A015095", "A015096", "A015097", "A015098", "A015099", "A015100", "A015102", "A015103", "A015105", "A015106", "A015107", "A015108", "A090192", "A227543", "A290789" ]
null
Olivier Gérard
2019-11-17T09:30:38
oeisdata/seq/A015/A015107.seq
3b7fe02ae3e806929cfa4dcbef1cd30d
A015108
Carlitz-Riordan q-Catalan numbers (recurrence version) for q=-11.
[ "1", "1", "-10", "-1231", "1636130", "23957879562", "-3858392581773300", "-6835385537899011365535", "133202313157282627679850238250", "28553099061411464607955930776882965774" ]
[ "sign" ]
31
0
3
[ "A000108", "A015083", "A015084", "A015085", "A015086", "A015089", "A015091", "A015092", "A015093", "A015095", "A015096", "A015097", "A015098", "A015099", "A015100", "A015102", "A015103", "A015105", "A015106", "A015107", "A015108", "A090192", "A227543", "A290789" ]
null
Olivier Gérard
2019-11-17T09:30:44
oeisdata/seq/A015/A015108.seq
11ffed320cc5670d4bcb09776b5c6212
A015109
Triangle of Gaussian (or q-binomial) coefficients for q = -2.
[ "1", "1", "1", "1", "-1", "1", "1", "3", "3", "1", "1", "-5", "15", "-5", "1", "1", "11", "55", "55", "11", "1", "1", "-21", "231", "-385", "231", "-21", "1", "1", "43", "903", "3311", "3311", "903", "43", "1", "1", "-85", "3655", "-25585", "56287", "-25585", "3655", "-85", "1", "1", "171", "14535", "208335", "875007", "875007", "208335", "14535", "171", "1", "1", "-341", "58311" ]
[ "sign", "tabl", "easy" ]
57
0
8
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A015152", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2022-09-08T08:44:39
oeisdata/seq/A015/A015109.seq
e052cf290523ed8ef2bc46a0ed501ac8
A015110
Triangle of q-binomial coefficients for q=-3.
[ "1", "1", "1", "1", "-2", "1", "1", "7", "7", "1", "1", "-20", "70", "-20", "1", "1", "61", "610", "610", "61", "1", "1", "-182", "5551", "-15860", "5551", "-182", "1", "1", "547", "49777", "433771", "433771", "49777", "547", "1", "1", "-1640", "448540", "-11662040", "35569222", "-11662040", "448540", "-1640", "1", "1", "4921", "4035220", "315323620" ]
[ "sign", "tabl", "easy" ]
13
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2012-11-04T10:44:17
oeisdata/seq/A015/A015110.seq
0045da0f7f43da694099e7d9d0f9b705
A015111
Inverse of 1102nd cyclotomic polynomial.
[ "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
16
0
1
null
null
Simon Plouffe
2017-07-15T13:29:29
oeisdata/seq/A015/A015111.seq
8ad93eba540aedcdb6923c98a2f1dbf2
A015112
Triangle of q-binomial coefficients for q=-4.
[ "1", "1", "1", "1", "-3", "1", "1", "13", "13", "1", "1", "-51", "221", "-51", "1", "1", "205", "3485", "3485", "205", "1", "1", "-819", "55965", "-219555", "55965", "-819", "1", "1", "3277", "894621", "14107485", "14107485", "894621", "3277", "1", "1", "-13107", "14317213", "-901984419", "3625623645", "-901984419", "14317213", "-13107", "1", "1" ]
[ "sign", "tabl", "easy" ]
14
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2015-06-10T18:17:56
oeisdata/seq/A015/A015112.seq
f09544a4d66d6c95034a4f3e27268791
A015113
Triangle of q-binomial coefficients for q=-5.
[ "1", "1", "1", "1", "-4", "1", "1", "21", "21", "1", "1", "-104", "546", "-104", "1", "1", "521", "13546", "13546", "521", "1", "1", "-2604", "339171", "-1679704", "339171", "-2604", "1", "1", "13021", "8476671", "210302171", "210302171", "8476671", "13021", "1", "1", "-65104", "211929796", "-26279294704", "131649159046" ]
[ "sign", "tabl", "easy" ]
12
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2016-04-09T10:52:11
oeisdata/seq/A015/A015113.seq
105b802c21038c2826454fdc458279c2
A015114
Inverse of 1105th cyclotomic polynomial.
[ "1", "-1", "0", "0", "0", "1", "-1", "0", "0", "0", "1", "-1", "0", "1", "-1", "1", "-1", "1", "0", "-1", "1", "-1", "1", "0", "-1", "1", "0", "0", "0", "-1", "2", "-1", "0", "0", "0", "1", "-1", "0", "0", "1", "0", "-1", "0", "1", "0", "0", "-1", "1", "0", "0", "0", "0", "1", "-1", "0", "0", "1", "0", "-1", "0", "1", "0", "0", "-1", "1", "0", "0", "0", "0", "1", "-1", "0", "0", "1", "0", "-1", "0", "1", "0", "0", "-1" ]
[ "sign" ]
13
0
31
null
null
Simon Plouffe
2019-03-25T17:20:01
oeisdata/seq/A015/A015114.seq
f0ffa448dbf65d5b42ab4e623d8df715
A015115
Inverse of 1106th cyclotomic polynomial.
[ "1", "-1", "1", "-1", "1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1" ]
[ "sign" ]
11
0
1
null
null
Simon Plouffe
2017-04-07T11:23:49
oeisdata/seq/A015/A015115.seq
6c544f467f1042cba66a0978b9c0ff7b
A015116
Triangle of q-binomial coefficients for q=-6.
[ "1", "1", "1", "1", "-5", "1", "1", "31", "31", "1", "1", "-185", "1147", "-185", "1", "1", "1111", "41107", "41107", "1111", "1", "1", "-6665", "1480963", "-8838005", "1480963", "-6665", "1", "1", "39991", "53308003", "1910490043", "1910490043", "53308003", "39991", "1", "1", "-239945", "1919128099", "-412612541285" ]
[ "sign", "tabl", "easy" ]
14
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2016-04-09T10:50:48
oeisdata/seq/A015/A015116.seq
29ec787ada64e6703ea143cb3c9b856f
A015117
Triangle of q-binomial coefficients for q=-7.
[ "1", "1", "1", "1", "-6", "1", "1", "43", "43", "1", "1", "-300", "2150", "-300", "1", "1", "2101", "105050", "105050", "2101", "1", "1", "-14706", "5149551", "-35927100", "5149551", "-14706", "1", "1", "102943", "252313293", "12328144851", "12328144851", "252313293", "102943", "1", "1", "-720600", "12363454300" ]
[ "sign", "tabl", "easy" ]
11
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2012-11-05T18:37:55
oeisdata/seq/A015/A015117.seq
63d94b23b6f3caa75af43e83f847f9e5
A015118
Triangle of q-binomial coefficients for q=-8.
[ "1", "1", "1", "1", "-7", "1", "1", "57", "57", "1", "1", "-455", "3705", "-455", "1", "1", "3641", "236665", "236665", "3641", "1", "1", "-29127", "15150201", "-120935815", "15150201", "-29127", "1", "1", "233017", "969583737", "61934287481", "61934287481", "969583737", "233017", "1", "1", "-1864135", "62053592185" ]
[ "sign", "tabl", "easy" ]
12
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2016-04-09T10:50:24
oeisdata/seq/A015/A015118.seq
7d02a2e2f35a13c05826c39bd7748dbc
A015119
Inverse of 1110th cyclotomic polynomial.
[ "1", "1", "0", "-1", "-1", "-1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "-1", "0", "1", "1", "1", "0", "-1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "1", "0", "-1", "-1", "-1", "0" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2021-11-20T10:46:38
oeisdata/seq/A015/A015119.seq
7c1bed14e1189508a2b923c869a54ccb
A015120
Inverse of 1111th cyclotomic polynomial.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
17
0
1
null
null
Simon Plouffe
2023-09-12T14:59:00
oeisdata/seq/A015/A015120.seq
ab20a4a5d0ede8d1103fe9637e40b0de
A015121
Triangle of q-binomial coefficients for q=-9.
[ "1", "1", "1", "1", "-8", "1", "1", "73", "73", "1", "1", "-656", "5986", "-656", "1", "1", "5905", "484210", "484210", "5905", "1", "1", "-53144", "39226915", "-352504880", "39226915", "-53144", "1", "1", "478297", "3177326971", "257015284435", "257015284435", "3177326971", "478297", "1", "1", "-4304672", "257363962948" ]
[ "sign", "tabl", "easy" ]
11
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2016-04-09T10:49:27
oeisdata/seq/A015/A015121.seq
b466dd09ab1e9efcac43a80ce0febc55
A015122
Inverse of 1113th cyclotomic polynomial.
[ "1", "-1", "0", "1", "-1", "0", "1", "0", "-1", "1", "0", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "0", "1", "-1", "0", "1", "0", "-1", "1", "0", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2017-08-11T17:29:23
oeisdata/seq/A015/A015122.seq
a1e8640617b288fe2006a6c05dd31266
A015123
Triangle of q-binomial coefficients for q=-10.
[ "1", "1", "1", "1", "-9", "1", "1", "91", "91", "1", "1", "-909", "9191", "-909", "1", "1", "9091", "918191", "918191", "9091", "1", "1", "-90909", "91828191", "-917272809", "91828191", "-90909", "1", "1", "909091", "9182728191", "917364637191", "917364637191", "9182728191", "909091", "1", "1", "-9090909", "918273728191" ]
[ "sign", "tabl", "easy" ]
11
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2016-04-09T10:49:57
oeisdata/seq/A015/A015123.seq
61b2f0baaaf8a002de882e0710c9ccfa
A015124
Triangle of q-binomial coefficients for q=-11.
[ "1", "1", "1", "1", "-10", "1", "1", "111", "111", "1", "1", "-1220", "13542", "-1220", "1", "1", "13421", "1637362", "1637362", "13421", "1", "1", "-147630", "198134223", "-2177691460", "198134223", "-147630", "1", "1", "1623931", "23974093353", "2898705467483", "2898705467483", "23974093353", "1623931", "1", "1" ]
[ "sign", "tabl", "easy" ]
7
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2012-11-05T18:56:32
oeisdata/seq/A015/A015124.seq
a270c21b4866b5c1c3082f7277bdbd5e
A015125
Triangle of q-binomial coefficients for q=-12.
[ "1", "1", "1", "1", "-11", "1", "1", "133", "133", "1", "1", "-1595", "19285", "-1595", "1", "1", "19141", "2775445", "2775445", "19141", "1", "1", "-229691", "399683221", "-4793193515", "399683221", "-229691", "1", "1", "2756293", "57554154133", "8283038077141", "8283038077141", "57554154133", "2756293", "1", "1" ]
[ "sign", "tabl", "easy" ]
8
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2012-11-05T19:04:25
oeisdata/seq/A015/A015125.seq
cb60d07e14e223ecd14339c035d233b4
A015126
Least k such that phi(k) = phi(n).
[ "1", "1", "3", "3", "5", "3", "7", "5", "7", "5", "11", "5", "13", "7", "15", "15", "17", "7", "19", "15", "13", "11", "23", "15", "25", "13", "19", "13", "29", "15", "31", "17", "25", "17", "35", "13", "37", "19", "35", "17", "41", "13", "43", "25", "35", "23", "47", "17", "43", "25", "51", "35", "53", "19", "41", "35", "37", "29", "59", "17", "61", "31", "37", "51", "65", "25", "67", "51", "69", "35", "71", "35", "73" ]
[ "nonn", "look" ]
24
1
3
[ "A000010", "A002181", "A015126", "A028476", "A066412", "A066659", "A143510" ]
null
Vladeta Jovovic, Jan 12 2002
2024-11-14T05:53:25
oeisdata/seq/A015/A015126.seq
3629052cbca5667f34b0f7aab8733216
A015127
Inverse of 1118th cyclotomic polynomial.
[ "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
11
0
1
null
null
Simon Plouffe
2017-04-07T11:26:22
oeisdata/seq/A015/A015127.seq
b5552615d482061ff8a4001056ea064e
A015128
Number of overpartitions of n: an overpartition of n is an ordered sequence of nonincreasing integers that sum to n, where the first occurrence of each integer may be overlined.
[ "1", "2", "4", "8", "14", "24", "40", "64", "100", "154", "232", "344", "504", "728", "1040", "1472", "2062", "2864", "3948", "5400", "7336", "9904", "13288", "17728", "23528", "31066", "40824", "53408", "69568", "90248", "116624", "150144", "192612", "246256", "313808", "398640", "504886", "637592", "802936", "1008448" ]
[ "nonn", "easy", "nice" ]
264
0
2
[ "A002448", "A002513", "A004402", "A014968", "A015128", "A022567", "A035363", "A106507", "A156616", "A261386", "A265835", "A284592", "A303662", "A321884" ]
null
N. J. A. Sloane
2025-02-16T08:32:33
oeisdata/seq/A015/A015128.seq
dac484fb8f71651db1eeb0e8d60b3f01
A015129
Triangle of (Gaussian) q-binomial coefficients for q = -13.
[ "1", "1", "1", "1", "-12", "1", "1", "157", "157", "1", "1", "-2040", "26690", "-2040", "1", "1", "26521", "4508570", "4508570", "26521", "1", "1", "-344772", "761974851", "-9900819720", "761974851", "-344772", "1", "1", "4482037", "128773405047", "21752862899691", "21752862899691", "128773405047", "4482037", "1" ]
[ "sign", "tabl", "easy" ]
27
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2022-09-08T08:44:39
oeisdata/seq/A015/A015129.seq
25efb065058fcd343edec7cb8f72fc24
A015130
Inverse of 1121st cyclotomic polynomial.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1" ]
[ "sign" ]
17
0
1
null
null
Simon Plouffe
2018-07-08T13:45:01
oeisdata/seq/A015/A015130.seq
a733691f2b09099a7140053e4b9de670
A015131
Inverse of 1122nd cyclotomic polynomial.
[ "1", "1", "0", "-1", "-1", "0", "1", "1", "0", "-1", "-1", "-1", "0", "1", "1", "0", "-1", "-2", "-1", "1", "2", "1", "0", "-1", "-1", "0", "1", "1", "1", "0", "-1", "-1", "0", "1", "2", "1", "-1", "-2", "-1", "0", "1", "1", "0", "-1", "-1", "-1", "0", "1", "1", "0", "-1", "-1", "0", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
16
0
18
null
null
Simon Plouffe
2025-05-10T16:34:49
oeisdata/seq/A015/A015131.seq
ce844cce6edc2b45056c6b9a6e72d030
A015132
Triangle of (Gaussian) q-binomial coefficients for q=-14.
[ "1", "1", "1", "1", "-13", "1", "1", "183", "183", "1", "1", "-2561", "36051", "-2561", "1", "1", "35855", "7063435", "7063435", "35855", "1", "1", "-501969", "1384469115", "-19375002205", "1384469115", "-501969", "1", "1", "7027567", "271355444571", "53166390519635", "53166390519635", "271355444571" ]
[ "sign", "tabl", "easy" ]
7
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2012-11-05T19:17:16
oeisdata/seq/A015/A015132.seq
470d0f8d104a5b5534c379fc656f6ab7
A015133
Triangle of (Gaussian) q-binomial coefficients for q=-15.
[ "1", "1", "1", "1", "-14", "1", "1", "211", "211", "1", "1", "-3164", "47686", "-3164", "1", "1", "47461", "10726186", "10726186", "47461", "1", "1", "-711914", "2413439311", "-36190151564", "2413439311", "-711914", "1", "1", "10678711", "543023133061", "122144174967811", "122144174967811", "543023133061" ]
[ "sign", "tabl", "easy" ]
16
0
5
[ "A015109", "A015110", "A015112", "A015113", "A015116", "A015117", "A015118", "A015121", "A015123", "A015124", "A015125", "A015129", "A015132", "A015133", "A022166", "A022167", "A022168", "A022169", "A022170", "A022171", "A022172", "A022173", "A022174", "A022175", "A022176", "A022177", "A022178", "A022179", "A022180", "A022181", "A022182", "A022183", "A022184", "A022185", "A022186", "A022187", "A022188" ]
null
Olivier Gérard
2020-11-24T06:33:46
oeisdata/seq/A015/A015133.seq
9c7d0b98419842d8b85edb08997cd013
A015134
Consider Fibonacci-type sequences b(0)=X, b(1)=Y, b(k)=b(k-1)+b(k-2) mod n; all are periodic; sequence gives number of distinct periods.
[ "1", "2", "2", "4", "3", "4", "4", "8", "5", "6", "14", "10", "7", "8", "12", "16", "9", "16", "22", "16", "29", "28", "12", "30", "13", "14", "14", "22", "63", "24", "34", "32", "39", "34", "30", "58", "19", "86", "32", "52", "43", "58", "22", "78", "39", "46", "70", "102", "25", "26", "42", "40", "27", "52", "160", "74", "63", "126", "62", "70", "63", "134", "104", "64", "57", "78", "34", "132", "101", "60", "74", "222" ]
[ "nonn" ]
88
1
2
[ "A015134", "A015135", "A106306" ]
null
Phil Carmody
2024-09-11T00:54:57
oeisdata/seq/A015/A015134.seq
559d4554b0f55108bdd9b35bcb95e478
A015135
Consider Fibonacci-type sequences f(0)=X, f(1)=Y, f(k)=f(k-1)+f(k-2) mod n; all are periodic; sequence gives number of distinct periods.
[ "1", "2", "2", "3", "3", "4", "2", "4", "3", "6", "3", "5", "2", "4", "5", "5", "2", "4", "3", "7", "3", "6", "2", "6", "4", "4", "4", "5", "3", "10", "3", "6", "5", "3", "5", "5", "2", "4", "4", "7", "2", "6", "2", "7", "7", "3", "2", "6", "3", "8", "4", "5", "2", "5", "5", "6", "5", "6", "3", "11", "2", "4", "5", "7", "5", "10", "2", "4", "3", "10", "3", "6", "2", "4", "7", "5", "5", "8", "3", "9", "5", "4", "2", "7", "5", "4", "5", "9", "2", "10", "4", "4", "5", "4", "7", "7", "2", "6", "7", "9", "3", "6", "2" ]
[ "nonn" ]
20
1
2
[ "A015134", "A015135", "A106306" ]
null
Phil Carmody
2025-02-16T08:32:33
oeisdata/seq/A015/A015135.seq
18ccba90d62c0bcadb2b409454facdfb
A015136
Consider Fibonacci-type sequences b(0)=X, b(1)=Y, b(k) = (b(k-1) + b(k-2)) mod n; all are periodic; sequence gives minimal nontrivial period.
[ "1", "3", "8", "3", "4", "3", "16", "3", "8", "3", "5", "3", "28", "3", "4", "3", "36", "3", "9", "3", "8", "3", "48", "3", "4", "3", "8", "3", "7", "3", "15", "3", "5", "3", "4", "3", "76", "3", "8", "3", "40", "3", "88", "3", "4", "3", "32", "3", "16", "3", "8", "3", "108", "3", "4", "3", "8", "3", "29", "3", "60", "3", "8", "3", "4", "3", "136", "3", "8", "3", "35", "3", "148", "3", "4", "3", "5", "3", "39", "3", "8", "3", "168", "3", "4", "3", "7", "3", "44", "3", "16", "3", "8", "3" ]
[ "nonn" ]
10
1
2
null
null
Phil Carmody
2023-11-19T01:33:58
oeisdata/seq/A015/A015136.seq
f6cf2fcfb9ea08da4c1c3bad5aa0228f
A015137
Consider Fibonacci-type sequences b(0)=X, b(1)=Y, b(k)=b(k-1)+b(k-2) mod n; all are periodic; sequence gives number of nontrivial periods of minimal length.
[ "1", "1", "1", "1", "1", "1", "3", "1", "1", "1", "2", "1", "6", "1", "1", "1", "8", "1", "2", "1", "1", "1", "11", "1", "1", "1", "1", "1", "4", "1", "2", "1", "2", "1", "1", "1", "18", "1", "1", "1", "42", "1", "21", "1", "1", "1", "69", "1", "3", "1", "1", "1", "26", "1", "1", "1", "1", "1", "2", "1", "62", "1", "1", "1", "1", "1", "33", "1", "1", "1", "2", "1", "36", "1", "1", "1", "2", "1", "2", "1", "1", "1", "41", "1", "1", "1", "4", "1", "180", "1", "3", "1", "1", "1", "1", "1", "48", "1", "2", "1" ]
[ "nonn" ]
5
1
7
null
null
Phil Carmody
2012-03-31T10:23:25
oeisdata/seq/A015/A015137.seq
57e600983162361f8451e682aebbc5fc
A015138
Consider Fibonacci-type sequences b(0)=X, b(1)=Y, b(k)=b(k-1)+b(k-2) mod n; all are periodic; sequence gives number of maximal length periods.
[ "1", "1", "1", "2", "1", "1", "3", "4", "3", "1", "11", "5", "6", "3", "4", "8", "8", "13", "19", "5", "27", "11", "11", "21", "5", "6", "9", "15", "58", "4", "31", "16", "24", "32", "12", "53", "18", "76", "24", "21", "42", "27", "21", "59", "12", "44", "69", "93", "21", "5", "32", "30", "26", "36", "145", "63", "40", "58", "59", "20", "62", "124", "72", "32", "24", "24", "33", "128", "99", "12", "71", "213", "36", "18", "20", "316" ]
[ "nonn" ]
5
1
4
null
null
Phil Carmody
2012-03-31T10:23:25
oeisdata/seq/A015/A015138.seq
67755429fd7a1cc06559e230800ab04a
A015139
Triangle of (Gaussian) q-binomial coefficients for q=-16.
[ "1", "1", "1", "1", "-15", "1", "1", "241", "241", "1", "1", "-3855", "61937", "-3855", "1", "1", "61681", "15852017", "15852017", "61681", "1", "1", "-986895", "4058178033", "-64914009615", "4058178033", "-986895", "1", "1", "15790321", "1038892589553", "265891841561073", "265891841561073" ]
[ "sign", "tabl", "easy" ]
4
0
5
null
null
Olivier Gérard
2012-03-30T17:20:37
oeisdata/seq/A015/A015139.seq
f72b41fe7d31299bfe03e8ff5338d058
A015140
Inverse of 1131st cyclotomic polynomial.
[ "1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "1", "0", "-1", "1", "0", "-1", "1", "0", "-1", "1", "0", "-1", "1", "0", "0", "0", "0", "1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "1", "0", "-1", "1", "0", "-1", "1", "0", "-1", "1", "0", "-1", "1", "0", "0", "0", "0", "1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "1", "0", "-1", "1", "0", "-1", "1", "0", "-1", "1", "0" ]
[ "sign" ]
16
0
1
null
null
Simon Plouffe
2022-04-14T09:59:22
oeisdata/seq/A015/A015140.seq
6d0778860fbc3519f10f127c1ae2d857
A015141
Triangle of (Gaussian) q-binomial coefficients for q=-17.
[ "1", "1", "1", "1", "-16", "1", "1", "273", "273", "1", "1", "-4640", "79170", "-4640", "1", "1", "78881", "22875490", "22875490", "78881", "1", "1", "-1340976", "6611095491", "-112364406880", "6611095491", "-1340976", "1", "1", "22796593", "1910605255923", "552052942096931", "552052942096931" ]
[ "sign", "tabl", "easy" ]
4
0
5
null
null
Olivier Gérard
2012-03-30T17:20:37
oeisdata/seq/A015/A015141.seq
3bf18d9afde77aeef25c0c25811dd885
A015142
Inverse of 1133rd cyclotomic polynomial.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
15
0
1
null
null
Simon Plouffe
2017-04-07T11:28:49
oeisdata/seq/A015/A015142.seq
60d15f6b98b554e405d942e3cc48feef
A015143
Triangle of (Gaussian) q-binomial coefficients for q=-18.
[ "1", "1", "1", "1", "-17", "1", "1", "307", "307", "1", "1", "-5525", "99775", "-5525", "1", "1", "99451", "32321575", "32321575", "99451", "1", "1", "-1790117", "10472289751", "-188467103825", "10472289751", "-1790117", "1", "1", "32222107", "3393020089207", "1099150621797151", "1099150621797151" ]
[ "sign", "tabl", "easy" ]
4
0
5
null
null
Olivier Gérard
2012-03-30T17:20:37
oeisdata/seq/A015/A015143.seq
f62fb981e8efe91c294759227e6df05e
A015144
Triangle of (Gaussian) q-binomial coefficients for q=-19.
[ "1", "1", "1", "1", "-18", "1", "1", "343", "343", "1", "1", "-6516", "124166", "-6516", "1", "1", "123805", "44817410", "44817410", "123805", "1", "1", "-2352294", "16179208815", "-307357797780", "16179208815", "-2352294", "1", "1", "44693587", "5840692029921", "2108183314181835", "2108183314181835" ]
[ "sign", "tabl", "easy" ]
4
0
5
null
null
Olivier Gérard
2012-03-30T17:20:37
oeisdata/seq/A015/A015144.seq
ccfe126387019e21127a35d5d14fe39d
A015145
Triangle of (Gaussian) q-binomial coefficients for q=-20.
[ "1", "1", "1", "1", "-19", "1", "1", "381", "381", "1", "1", "-7619", "152781", "-7619", "1", "1", "152381", "61104781", "61104781", "152381", "1", "1", "-3047619", "24442064781", "-488777143219", "24442064781", "-3047619", "1", "1", "60952381", "9776822864781", "3910241587816781", "3910241587816781" ]
[ "sign", "tabl", "easy" ]
4
0
5
null
null
Olivier Gérard
2012-03-30T17:20:37
oeisdata/seq/A015/A015145.seq
b354bfcce3edca763729dc007c19fc2a
A015146
Triangle of (Gaussian) q-binomial coefficients for q=-21.
[ "1", "1", "1", "1", "-20", "1", "1", "421", "421", "1", "1", "-8840", "186082", "-8840", "1", "1", "185641", "82053322", "82053322", "185641", "1", "1", "-3898460", "36185700643", "-759813761720", "36185700643", "-3898460", "1", "1", "81867661", "15957890085103", "7036671432989563" ]
[ "sign", "tabl", "easy" ]
6
0
5
null
null
Olivier Gérard
2022-10-16T09:03:40
oeisdata/seq/A015/A015146.seq
c1891fb1ef4fcf4606bebbc89c88cfb4
A015147
Triangle of (Gaussian) q-binomial coefficients for q=-22.
[ "1", "1", "1", "1", "-21", "1", "1", "463", "463", "1", "1", "-10185", "224555", "-10185", "1", "1", "224071", "108674435", "108674435", "224071", "1", "1", "-4929561", "52598650611", "-1157056709445", "52598650611", "-4929561", "1", "1", "108450343", "25457741966163", "12320392440820971" ]
[ "sign", "tabl", "easy" ]
6
0
5
null
null
Olivier Gérard
2021-04-11T11:13:26
oeisdata/seq/A015/A015147.seq
0bb3aaf73f7e2f499a79f62441372d7e
A015148
Inverse of 1139th cyclotomic polynomial.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2023-01-10T19:16:44
oeisdata/seq/A015/A015148.seq
bfd953a7ea7ab9f4b830c241bfd57fc2
A015149
Inverse of 1140th cyclotomic polynomial.
[ "1", "0", "1", "0", "0", "0", "-1", "0", "-1", "0", "-1", "0", "0", "0", "1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "1", "0", "1", "0", "1", "0", "0", "0", "-1", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "1", "0", "0" ]
[ "sign" ]
11
0
1
null
null
Simon Plouffe
2017-04-07T11:30:16
oeisdata/seq/A015/A015149.seq
613aac81b540991068bc40ea776ce1c1
A015150
Triangle of (Gaussian) q-binomial coefficients for q=-23.
[ "1", "1", "1", "1", "-22", "1", "1", "507", "507", "1", "1", "-11660", "268710", "-11660", "1", "1", "268181", "142135930", "142135930", "268181", "1", "1", "-6168162", "75190175151", "-1729225724380", "75190175151", "-6168162", "1", "1", "141867727", "39775596486717", "21039564578706611" ]
[ "sign", "tabl", "easy" ]
4
0
5
null
null
Olivier Gérard
2012-03-30T17:20:37
oeisdata/seq/A015/A015150.seq
1aede5dd1a7bead41766c3aba00c66d5
A015151
Triangle of (Gaussian) q-binomial coefficients for q=-24.
[ "1", "1", "1", "1", "-23", "1", "1", "553", "553", "1", "1", "-13271", "319081", "-13271", "1", "1", "318505", "183777385", "183777385", "318505", "1", "1", "-7644119", "105856092265", "-2540354792855", "105856092265", "-7644119", "1", "1", "183458857", "60973101500521", "35117970512519785" ]
[ "sign", "tabl", "easy" ]
4
0
5
null
null
Olivier Gérard
2012-03-30T17:20:37
oeisdata/seq/A015/A015151.seq
5bfca3b565f082f9ff28442be4374655
A015152
Sum of (Gaussian) q-binomial coefficients for q=-2.
[ "1", "2", "1", "8", "7", "134", "37", "8516", "12259", "2196098", "-1896671", "2242814912", "8371908703", "9201070882046", "-50188906239587", "150640766448080444", "1945921801461187291", "9876134472777874272122", "-235305539337366453248999" ]
[ "sign" ]
10
0
2
null
null
Olivier Gérard
2012-10-23T17:42:37
oeisdata/seq/A015/A015152.seq
109a839f1e0605a39ecdf441ca95198f
A015153
Inverse of 1144th cyclotomic polynomial.
[ "1", "0", "0", "0", "-1", "0", "0", "0", "1", "0", "0", "0", "-1", "0", "0", "0", "1", "0", "0", "0", "-1", "0", "0", "0", "1", "0", "0", "0", "-1", "0", "0", "0", "1", "0", "0", "0", "-1", "0", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0", "0", "-1", "0", "0", "0", "1", "0", "0", "0", "-1", "0", "0", "0", "1", "0", "0", "0", "-1", "0", "0", "0", "1", "0", "0", "0", "-1" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2024-05-28T12:54:38
oeisdata/seq/A015/A015153.seq
6e35aa83037a1e545ce068730be9bbc4
A015154
Sum of (Gaussian) q-binomial coefficients for q=-3.
[ "1", "2", "0", "16", "32", "1344", "-5120", "968192", "13138944", "6377617408", "-245871738880", "376093809229824", "44307874417573888", "199959909725932814336", "-70241187753472205783040", "956261367126518476707463168" ]
[ "sign" ]
8
0
2
null
null
Olivier Gérard
2012-10-23T17:42:52
oeisdata/seq/A015/A015154.seq
dbee3683c14017db8bf994dce7e8fd4c
A015155
Sum of (Gaussian) q-binomial coefficients for q=-4.
[ "1", "2", "-1", "28", "121", "7382", "-109261", "30010768", "1850263021", "1970456206922", "-481096287226201", "2065208924598783748", "2021994980843488552801", "34652498137874270655807422", "-135624483203827510877656066021" ]
[ "sign" ]
8
0
2
null
null
Olivier Gérard
2012-10-23T17:41:39
oeisdata/seq/A015/A015155.seq
6e77ed860b81132d908a59a385a622ef
A015156
Inverse of 1147th cyclotomic polynomial.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2017-04-07T11:31:31
oeisdata/seq/A015/A015156.seq
8cde2e4fa4a76035fbd3a90632f8df76
A015157
Inverse of 1148th cyclotomic polynomial.
[ "1", "0", "-1", "0", "1", "0", "-1", "0", "1", "0", "-1", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2017-04-07T11:32:24
oeisdata/seq/A015/A015157.seq
8bd560783ae61cdd55f272a2a4aaf571
A015158
Theta series of 17-dimensional lattice Q_17(6).
[ "1", "0", "2040", "41956", "362406", "1933920", "7591792", "24124428", "65640978", "158815904", "350243520", "715382916", "1373241708", "2505490464", "4367865216", "7321237204", "11884992774", "18736213536", "28751284680", "43126730772", "63361584408", "91360506752", "129562966320", "180742158696", "248590240202", "337956307872" ]
[ "nonn" ]
37
0
3
[ "A015158", "A015159", "A015160", "A015161", "A015162", "A015163", "A015164", "A015165" ]
null
N. J. A. Sloane
2018-12-07T12:29:22
oeisdata/seq/A015/A015158.seq
0f840fa2fdc569f37df12bf6cf05572f
A015159
Theta series of 17-dimensional lattice Q_17(6)^{+2}.
[ "1", "0", "0", "0", "0", "0", "0", "816", "2040", "0", "0", "20400", "41956", "0", "0", "236912", "362406", "0", "0", "1236240", "1933920", "0", "0", "5861328", "7591792", "0", "0", "17201280", "24124428", "0", "0", "55003296", "65640978", "0", "0", "120568080", "158815904", "0", "0", "307510960", "350243520", "0", "0", "564643440", "715382916", "0", "0", "1246785984", "1373241708", "0", "0" ]
[ "nonn" ]
30
0
8
[ "A015158", "A015159", "A015160", "A015161", "A015162", "A015163", "A015164", "A015165" ]
null
N. J. A. Sloane
2018-12-24T09:11:39
oeisdata/seq/A015/A015159.seq
3218f75f80e6cc190d4f9590780bbd98
A015160
Theta series of 17-dimensional lattice Q_17(6)^{+3}.
[ "1", "0", "0", "0", "0", "1020", "2040", "0", "34782", "41956", "0", "376992", "362406", "0", "2306832", "1933920", "0", "9891384", "7591792", "0", "33439476", "24124428", "0", "95442624", "65640978", "0", "239451936", "158815904", "0", "542842980", "350243520", "0", "1135694622", "715382916", "0", "2225152032", "1373241708", "0", "4123291248", "2505490464", "0", "7286817984", "4367865216", "0", "12375237108", "7321237204", "0", "20304913152", "11884992774", "0", "32294964192", "18736213536" ]
[ "nonn" ]
31
0
6
[ "A015158", "A015159", "A015160", "A015161", "A015162", "A015163", "A015164", "A015165" ]
null
N. J. A. Sloane
2018-12-07T12:30:04
oeisdata/seq/A015/A015160.seq
e1c9e167df9a65f3e9232a92af7225f0
A015161
Theta series of 17-dimensional lattice Q_17(6)^{+6}.
[ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "240", "0", "0", "1020", "816", "0", "0", "2040", "0", "0", "0", "0", "17952", "0", "0", "34782", "20400", "0", "0", "41956", "0", "0", "0", "0", "208080", "0", "0", "376992", "236912", "0", "0", "362406", "0", "0", "0", "0", "1618944", "0", "0", "2306832", "1236240", "0", "0", "1933920", "0", "0", "0", "0", "6613680", "0", "0", "9891384", "5861328", "0", "0", "7591792", "0", "0", "0", "0", "26689728", "0", "0", "33439476", "17201280", "0", "0", "24124428", "0", "0", "0", "0", "69759840", "0", "0", "95442624", "55003296", "0", "0", "65640978", "0", "0", "0", "0", "204207264" ]
[ "nonn" ]
25
0
18
[ "A015158", "A015159", "A015160", "A015161", "A015162", "A015163", "A015164", "A015165" ]
null
N. J. A. Sloane
2018-12-07T12:30:22
oeisdata/seq/A015/A015161.seq
9d5ad65a28feebc1361b9550f9b7acf5
A015162
Theta series of 17-dimensional lattice Q'_17(6).
[ "1", "0", "1326", "31552", "240618", "1452480", "5030028", "18128256", "43527174", "119299200", "232127928", "537564480", "910537442", "1881950592", "2894860164", "5501926784", "7880557842", "14072683776", "19054928890", "32409323328", "42013951980", "68622996416", "85866810348", "135824277120", "164834073388", "253845438336", "300583037448" ]
[ "nonn" ]
30
0
3
[ "A015158", "A015159", "A015160", "A015161", "A015162", "A015163", "A015164", "A015165" ]
null
N. J. A. Sloane
2018-12-02T08:14:58
oeisdata/seq/A015/A015162.seq
f3f67925ee74f7bd0ef83124cbb6e7de
A015163
Theta series of 17-dimensional lattice Q'_17(6)^{+2}.
[ "1", "0", "0", "136", "1326", "8160", "31552", "88128", "240618", "658784", "1452480", "2622216", "5030028", "10390944", "18128256", "26822464", "43527174", "77769696", "119299200", "157895592", "232127928", "379052672", "537564480", "662425536", "910537442", "1402281312", "1881950592", "2201578336", "2894860164", "4268628192", "5501926784" ]
[ "nonn" ]
24
0
4
[ "A015158", "A015159", "A015160", "A015161", "A015162", "A015163", "A015164", "A015165" ]
null
N. J. A. Sloane
2018-12-07T12:30:32
oeisdata/seq/A015/A015163.seq
802a5be59503b984f6599a6f5f18e621
A015164
Theta series of 17-dimensional lattice Q'_17(6)^{+3}.
[ "1", "0", "0", "0", "102", "0", "1326", "9792", "0", "31552", "122196", "0", "240618", "992256", "0", "1452480", "4163742", "0", "5030028", "17109888", "0", "18128256", "45317988", "0", "43527174", "134013312", "0", "119299200", "276648888", "0", "232127928", "672628800", "0", "537564480", "1186603368", "0", "910537442", "2535618816", "0", "1881950592", "4014830772", "0", "2894860164", "7826947968", "0", "5501926784", "11452412304", "0", "7880557842", "20846939520", "0" ]
[ "nonn" ]
27
0
5
[ "A015158", "A015159", "A015160", "A015161", "A015162", "A015163", "A015164", "A015165" ]
null
N. J. A. Sloane
2018-12-07T12:30:50
oeisdata/seq/A015/A015164.seq
53d1ccb96e50d5145d39a4b74b49ff76
A015165
Theta series of 17-dimensional lattice Q'_17(6)^{+6}.
[ "1", "0", "0", "0", "0", "0", "0", "0", "102", "136", "0", "1632", "1326", "0", "9792", "8160", "0", "36144", "31552", "0", "122196", "88128", "0", "394944", "240618", "0", "992256", "658784", "0", "1991040", "1452480", "0", "4163742", "2622216", "0", "9238752", "5030028", "0", "17109888", "10390944", "0", "26670144", "18128256", "0", "45317988", "26822464", "0", "84237312", "43527174", "0", "134013312", "77769696", "0", "183149568", "119299200", "0", "276648888", "157895592", "0", "463739328", "232127928", "0", "672628800", "379052672", "0", "845519616", "537564480", "0", "1186603368", "662425536", "0" ]
[ "nonn" ]
25
0
9
[ "A015158", "A015159", "A015160", "A015161", "A015162", "A015163", "A015164", "A015165" ]
null
N. J. A. Sloane
2018-12-07T12:31:04
oeisdata/seq/A015/A015165.seq
fc7f789cc931792f6634b8c001a462a2
A015166
Inverse of 1157th cyclotomic polynomial.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2018-12-25T13:13:40
oeisdata/seq/A015/A015166.seq
9a221dfa3874a2d41557506b18643154
A015167
Sum of (Gaussian) q-binomial coefficients for q=-5.
[ "1", "2", "-2", "44", "340", "28136", "-1006568", "437583728", "79514299024", "171089734764320", "-154959265326020384", "1670488101437425694912", "7569711508409229239910208", "407849146892525224567929125504", "-9239554802939536369959859006659200" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-01T07:54:47
oeisdata/seq/A015/A015167.seq
23ecf4c71f99a465b6be21a47bfd90b0
A015168
Inverse of 1159th cyclotomic polynomial.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2017-04-07T11:34:37
oeisdata/seq/A015/A015168.seq
719ba5358f883feb06f5645e0ecbd00e
A015169
Sum of (Gaussian) q-binomial coefficients for q=-6.
[ "1", "2", "-3", "64", "779", "84438", "-5889407", "3927676076", "1656518279511", "6600296688949762", "-16680688702495266643", "399061333268551884767064", "6052502892664968398280203779", "868681765846316883728697065421998", "-79048150954572853311144873191795246247" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-01T07:54:41
oeisdata/seq/A015/A015169.seq
933becd052ea94b3edf03ed646803edf
A015170
Sum of (Gaussian) q-binomial coefficients for q=-7.
[ "1", "2", "-4", "88", "1552", "214304", "-25657408", "25161122176", "21180326658304", "145091197773521408", "-854412416885602518016", "40982963248858736353073152", "1689534488240076764899484766208", "567260343703475322245495898410786816" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-01T11:24:37
oeisdata/seq/A015/A015170.seq
2e04260239555d38bfeb1de943ae9e09
A015171
Inverse of 1162nd cyclotomic polynomial.
[ "1", "-1", "1", "-1", "1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
16
0
1
null
null
Simon Plouffe
2017-04-07T11:35:15
oeisdata/seq/A015/A015171.seq
74ab0736ae90e46c0aa8a9c046eae8e0
A015172
Sum of (Gaussian) q-binomial coefficients for q=-8.
[ "1", "2", "-5", "116", "2797", "480614", "-90693665", "125808208472", "190450108052689", "2111092262515670858", "-25557558806111498581565", "2266716939357158770139731004", "219542291935127655798395905040053" ]
[ "sign" ]
8
0
2
null
null
Olivier Gérard
2012-11-01T11:24:34
oeisdata/seq/A015/A015172.seq
f6baf258c6f610a4cd8eb4df4d477a97
A015173
Sum of (Gaussian) q-binomial coefficients for q=-9.
[ "1", "2", "-6", "148", "4676", "980232", "-274157336", "520386179408", "1312327085726736", "22403542811017395232", "-508377595506902032430176", "78115306822996588019507120448", "15953583859604206839297545233032256" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-01T11:24:31
oeisdata/seq/A015/A015173.seq
d144c197b7a3a4727363eb1595cae2f1
A015174
Sum of (Gaussian) q-binomial coefficients for q=-10.
[ "1", "2", "-7", "184", "7375", "1854566", "-733798243", "1853096548948", "7341689356896139", "185324336420417243330", "-7341318715564987522409479", "1853228681381416966904537937712", "734135578021202833790446696598284903" ]
[ "sign" ]
9
0
2
null
null
Olivier Gérard
2012-11-01T11:24:14
oeisdata/seq/A015/A015174.seq
2a727789abe8ed63519a7f9ad7fb0ca2
A015175
Inverse of 1166th cyclotomic polynomial.
[ "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2024-07-21T18:01:58
oeisdata/seq/A015/A015175.seq
69bb4da7a9dfee0065e580475f25797a
A015176
Sum of (Gaussian) q-binomial coefficients for q=-11.
[ "1", "2", "-8", "224", "11104", "3301568", "-1781718272", "5845362369536", "34732341146745856", "1253074795410176571392", "-81894537495135204112621568", "32501369235036890622758291800064", "23365532309472568981966918077606559744" ]
[ "sign" ]
13
0
2
null
null
Olivier Gérard
2024-08-04T16:39:23
oeisdata/seq/A015/A015176.seq
ccfd300ab9efc9872245e11ca2b5369a
A015177
Sum of (Gaussian) q-binomial coefficients for q=-12.
[ "1", "2", "-9", "268", "16097", "5589174", "-3994286453", "16681189975136", "143155871655133749", "7172892651869295403018", "-738638508197444971086627361", "444125129581255110369102906170292", "548815482754196320790032447578510162313", "3959865364571704158400109500272058863584565086" ]
[ "sign" ]
9
0
2
null
null
Olivier Gérard
2012-11-01T11:24:28
oeisdata/seq/A015/A015177.seq
ef4baf7c1f0e0f543555ddcaa01a0fae
A015178
Sum of (Gaussian) q-binomial coefficients for q=-13.
[ "1", "2", "-10", "316", "22612", "9070184", "-8377559560", "43763281573552", "525766973409879184", "35700104721503125675808", "-5575424140185495445892279200", "4921551444873804590294004874254784" ]
[ "sign" ]
9
0
2
null
null
Olivier Gérard
2012-11-01T11:24:22
oeisdata/seq/A015/A015178.seq
7a44e6ac6240807143e7d6b1fba4af1e
A015179
Inverse of 1170th cyclotomic polynomial.
[ "1", "0", "0", "1", "0", "0", "0", "0", "0", "-1", "0", "0", "-1", "0", "0", "-1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "0", "0", "-1", "0", "0", "0", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0", "0", "0", "0", "-1", "0", "0", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "0", "0" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2021-01-30T12:53:12
oeisdata/seq/A015/A015179.seq
ea9716a28bdde292700ed0d2e340583a
A015180
Sum of (Gaussian) q-binomial coefficients for q=-14.
[ "1", "2", "-11", "368", "30931", "14198582", "-16607067911", "106875505983548", "1750822987283505151", "157729203624081715477442", "-36173520194110711820168534651", "45623834026724887990209962768504648" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-01T11:24:25
oeisdata/seq/A015/A015180.seq
ce7902bb31e3f15093e79eea7f589925
A015181
Sum of (Gaussian) q-binomial coefficients for q=-15.
[ "1", "2", "-12", "424", "41360", "21547296", "-31364696768", "245374417559168", "5359443267044815104", "628878513018386722071040", "-206033745813261327767100673024", "362642628119601346053904604076582912" ]
[ "sign" ]
11
0
2
null
null
Olivier Gérard
2024-08-04T19:09:50
oeisdata/seq/A015/A015181.seq
7bf6ecc31241f2e553bcb14926d40eff
A015182
Inverse of 1173rd cyclotomic polynomial.
[ "1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "1", "-1", "0", "1", "-1", "1", "0", "-1", "1", "0", "-1", "2", "-1", "-1", "2", "-1", "-1", "2", "-1", "-1", "2", "-1", "0", "1", "-1", "0", "1", "-1", "1", "0", "-1", "1", "0", "-1", "2", "-1", "-1", "2", "-1", "-1", "2", "-1", "-1", "2", "-1", "0", "1", "-1", "0", "1", "-1", "1", "0", "-1", "1", "0", "-1", "1", "0", "-1", "1", "0", "-1", "1", "0", "-1", "1", "0", "0" ]
[ "sign" ]
17
0
24
null
null
Simon Plouffe
2017-04-07T11:37:11
oeisdata/seq/A015/A015182.seq
17b716dd9ad0a1a769a5642a87425f07
A015183
Sum of (Gaussian) q-binomial coefficients for q=-16.
[ "1", "2", "-13", "484", "54229", "31827398", "-56799627337", "533861499881896", "15248101644637051801", "2292948178255678956694922", "-1047836980355690810689170063493" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-01T11:05:28
oeisdata/seq/A015/A015183.seq
9b556431eaf890f5a1682397e1d83c48
A015184
Sum of (Gaussian) q-binomial coefficients for q=-17.
[ "1", "2", "-14", "548", "69892", "45908744", "-99144897848", "1107927140298896", "40685201771094371344", "7728712362321489784528928", "-4824756225502025532265653215456" ]
[ "sign" ]
9
0
2
null
null
Olivier Gérard
2012-11-02T02:23:22
oeisdata/seq/A015/A015184.seq
73ecaeeb1fecfa6fb8093bbffe0cf54a
A015185
Sum of (Gaussian) q-binomial coefficients for q=-18.
[ "1", "2", "-15", "616", "88727", "64842054", "-167526104555", "2205087348216932", "102567247433719984179", "24300180776276754627424258", "-20345117815692779870091092223535" ]
[ "sign" ]
8
0
2
null
null
Olivier Gérard
2012-11-02T02:23:04
oeisdata/seq/A015/A015185.seq
b394526e6076c14621294ee1c25ff6fe
A015186
Inverse of 1177th cyclotomic polynomial.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2017-04-07T11:37:54
oeisdata/seq/A015/A015186.seq
72d71d4d01b2ee60169c34ac146be1d7
A015187
Inverse of 1178th cyclotomic polynomial.
[ "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2023-02-20T10:40:40
oeisdata/seq/A015/A015187.seq
67f1b03fb7773e81b6a601f0973c1d25
A015188
Sum of (Gaussian) q-binomial coefficients for q=-19.
[ "1", "2", "-16", "688", "111136", "89882432", "-275004084736", "4228048101810688", "245826835826279382016", "71807813126925810352535552", "-79325152089697863954203470053376", "440258301458598565100624737135157198848" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-02T03:15:04
oeisdata/seq/A015/A015188.seq
dea8660293ae26c2e11498a5b09ebce8
A015189
Sum of (Gaussian) q-binomial coefficients for q=-20.
[ "1", "2", "-17", "764", "137545", "122514326", "-439899108893", "7840036943267888", "563086539896825644669", "200706071912897689508021450", "-288299907015593990815045809601769", "2055229599788057603302245120218872775012", "59043825067253137194943604004923346683555151793" ]
[ "sign" ]
10
0
2
null
null
Olivier Gérard
2012-11-02T02:23:07
oeisdata/seq/A015/A015189.seq
3071b9cd48e61fa61a74e15e147cb1b0
A015190
Sum of (Gaussian) q-binomial coefficients for q=-21.
[ "1", "2", "-18", "844", "168404", "164477928", "-687450157352", "14105258809884656", "1238186812120404030096", "533503696576292562518040352", "-983466011800819442632186373851168", "8898776193390263176983910297292084624064" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-02T02:23:57
oeisdata/seq/A015/A015190.seq
61cadd14f07a11ecba48eb33561ac28a
A015191
Sum of (Gaussian) q-binomial coefficients for q=-22.
[ "1", "2", "-19", "928", "204187", "217797014", "-1051869267343", "24691700582474956", "2623787788594827068839", "1354983886103558712414827138", "-3167615521223929914885937664998051", "35988261063301772968035157512367644041272" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-02T02:23:54
oeisdata/seq/A015/A015191.seq
5e75ca721234d9f0bdb59fd448eea06f
A015192
Sum of (Gaussian) q-binomial coefficients for q=-23.
[ "1", "2", "-20", "1016", "245392", "284808224", "-1578857710400", "42158680634122112", "5375819228502202503424", "3301498570201414782959518208", "-9682664507968948802598455253816320", "136769548174962732310329353951236926470144" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-02T02:23:49
oeisdata/seq/A015/A015192.seq
c3c9fa226c91413c8672007ccfefd06d
A015193
Sum of (Gaussian) q-binomial coefficients for q=-24.
[ "1", "2", "-21", "1108", "292541", "368191782", "-2328657896561", "70357887594958328", "10680463616952822186081", "7744687942631607006277071562", "-28215713826988856526068441288465101", "491039343653190447669922115080524942235548" ]
[ "sign" ]
7
0
2
null
null
Olivier Gérard
2012-11-02T02:23:45
oeisdata/seq/A015/A015193.seq
b51a4ce6dc1280f672a808fd059290ed
A015194
Inverse of 1185th cyclotomic polynomial.
[ "1", "-1", "0", "1", "-1", "1", "0", "-1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "1", "-1" ]
[ "sign" ]
13
0
1
null
null
Simon Plouffe
2017-04-07T11:39:09
oeisdata/seq/A015/A015194.seq
38b1a03c4bcb6846ccae3a7d75693c36
A015195
Sum of Gaussian binomial coefficients for q=9.
[ "1", "2", "12", "184", "9104", "1225248", "540023488", "652225844096", "2584219514040576", "28081351726592246272", "1001235747932175990213632", "97915621602690773814148184064", "31420034518763282871588038742544384", "27654326463468067495668136467306727743488" ]
[ "nonn" ]
20
0
2
[ "A006116", "A006117", "A006118", "A006119", "A006120", "A006121", "A006122", "A015195", "A022173" ]
null
N. J. A. Sloane, Olivier Gérard
2019-05-14T09:38:21
oeisdata/seq/A015/A015195.seq
530511a306abc875fa2a5ae79e8e4531
A015196
Sum of Gaussian binomial coefficients for q=10.
[ "1", "2", "13", "224", "13435", "2266646", "1348019857", "2269339773068", "13484735901526279", "226960944509263279490", "13485189809930561625032701", "2269636415245291711513986785912", "1348523520252401463276762566348539123" ]
[ "nonn" ]
20
0
2
[ "A006116", "A006117", "A006118", "A006119", "A006120", "A006121", "A006122", "A015195", "A015196", "A022174" ]
null
N. J. A. Sloane, Olivier Gérard
2019-05-14T09:38:28
oeisdata/seq/A015/A015196.seq
b39a71453007cd829e64d1873584d0cf
A015197
Sum of Gaussian binomial coefficients for q=11.
[ "1", "2", "14", "268", "19156", "3961832", "3092997464", "7024809092848", "60287817008722576", "1505950784990730735392", "142158530752430089391520224", "39060769254069395008311334483648", "40559566021977397260316290099710383936" ]
[ "nonn" ]
19
0
2
[ "A006116", "A006117", "A006118", "A006119", "A006120", "A006121", "A006122", "A015195", "A015196", "A015197", "A022175" ]
null
N. J. A. Sloane, Olivier Gérard
2019-05-14T09:38:35
oeisdata/seq/A015/A015197.seq
4a48cb87293272c037ba71020cc1e9f1
A015198
Inverse of 1189th cyclotomic polynomial.
[ "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "-1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "sign" ]
15
0
1
null
null
Simon Plouffe
2017-04-07T11:39:56
oeisdata/seq/A015/A015198.seq
406bcd42fe6edbb13d2c12b3ddbe7abf
A015199
Inverse of 1190th cyclotomic polynomial.
[ "1", "1", "0", "0", "0", "-1", "-1", "-1", "-1", "0", "1", "1", "1", "1", "1", "0", "-1", "-2", "-2", "-1", "0", "0", "1", "2", "2", "1", "0", "-1", "-1", "-1", "-1", "-1", "0", "1", "2", "2", "1", "0", "0", "-1", "-2", "-2", "-1", "0", "1", "1", "1", "1", "1", "0", "-1", "-2", "-2", "-1", "0", "0", "1", "2", "2", "1", "0", "-1", "-1", "-1", "-1", "-1", "0", "1", "2", "2", "1", "0", "0", "-1", "-2", "-2", "-1", "0", "1", "1", "1" ]
[ "sign" ]
17
0
18
null
null
Simon Plouffe
2017-06-25T12:57:39
oeisdata/seq/A015/A015199.seq
7e67ef36ae4cf57b6790ad687b2b316f
A015200
Sum of Gaussian binomial coefficients for q=12.
[ "1", "2", "15", "316", "26537", "6605334", "6616438915", "19736647911152", "237118435525391709", "8486871559326397146058", "1223496018226895154470801975", "525487164444668938421129856286884", "909068834019126312744002601418684280593" ]
[ "nonn" ]
15
0
2
[ "A015200", "A022176" ]
null
N. J. A. Sloane, Olivier Gérard
2019-05-14T09:38:42
oeisdata/seq/A015/A015200.seq
e696cf0ef30e694a2551d580b8f1361a