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
2.31k
offset_a
int64
-14,827
666,262,453B
offset_b
int64
0
635M
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cross_references
listlengths
1
128
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former_ids
listlengths
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author
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231
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timestamp
timestamp[us]date
1999-12-11 03:00:00
2025-04-28 00:58:08
filename
stringlengths
29
29
hash
stringlengths
32
32
A009101
Fixed point when iterating the function f on n, where f(x) = x + product of digits of x.
[ "0", "102", "102", "102", "102", "10", "102", "102", "102", "102", "10", "102", "102", "102", "102", "20", "102", "102", "102", "60", "20", "110", "102", "110", "102", "50", "102", "140", "60", "110", "30", "70", "102", "50", "70", "50", "102", "170", "102", "102", "40", "140", "50", "80", "60", "140", "70", "110", "80", "150", "50", "170", "102", "202", "102", "80", "170", "110", "170" ]
[ "nonn", "base" ]
42
0
2
[ "A007954", "A009101", "A230099" ]
null
David W. Wilson
2023-01-09T08:42:02
oeisdata/seq/A009/A009101.seq
bb1b1398ed69d84800f4ed026f1f7e24
A009102
Expansion of e.g.f. cos(x)/(1+x).
[ "1", "-1", "1", "-3", "13", "-65", "389", "-2723", "21785", "-196065", "1960649", "-21567139", "258805669", "-3364473697", "47102631757", "-706539476355", "11304631621681", "-192178737568577", "3459217276234385", "-65725128248453315", "1314502564969066301" ]
[ "sign", "easy" ]
64
0
4
[ "A000023", "A000142", "A000166", "A000522", "A009102", "A009551", "A010844", "A053486" ]
null
R. H. Hardin
2025-02-16T08:32:32
oeisdata/seq/A009/A009102.seq
b8c329c25bd62d267bad0d7212bf7428
A009103
Expansion of e.g.f. cos(x)/cos(log(1+x)).
[ "1", "0", "0", "-3", "11", "-70", "534", "-4725", "47753", "-542988", "6859084", "-95298995", "1444301715", "-23711336922", "419190167434", "-7939747234965", "160403009819921", "-3442962495033400", "78246246638467512", "-1877007578925506787" ]
[ "sign", "easy" ]
18
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009103.seq
71b6cc348c546827bf743d616da8730b
A009104
Expansion of e.g.f. cos(x)/cos(sin(x)), even powers only.
[ "1", "0", "-4", "-24", "272", "14528", "181312", "-20265088", "-1771263744", "-4388386816", "16325400792064", "1796402984175616", "-109123852786069504", "-68488660591133114368", "-7567377513364063567872" ]
[ "sign" ]
16
0
3
null
null
R. H. Hardin
2018-07-26T08:04:30
oeisdata/seq/A009/A009104.seq
eaaebef32b344a71020d9dcfe3ec99cb
A009105
Expansion of e.g.f. cos(x)/cos(sinh(x)), even powers only.
[ "1", "0", "4", "56", "2192", "128448", "11141824", "1332816512", "210250492160", "42290401757184", "10563624419906560", "3208072210301966336", "1164053448822395604992", "497366043438147538010112", "247165485059674632625438720" ]
[ "nonn" ]
16
0
3
null
null
R. H. Hardin
2018-07-26T08:04:37
oeisdata/seq/A009/A009105.seq
f8c6efbbe09d77760250d58131ceac7d
A009106
Expansion of e.g.f. cos(x)/cos(tan(x)), even powers only.
[ "1", "0", "8", "216", "12032", "1075328", "140944000", "25464568832", "6065774456832", "1842040163078144", "694620312112857088", "318448731218429771776", "174429761567957718302720", "112504917152076237383401472" ]
[ "nonn" ]
16
0
3
null
null
R. H. Hardin
2018-07-26T08:04:43
oeisdata/seq/A009/A009106.seq
fe1e7e66f01824559c84ba742216ee0f
A009107
Expansion of e.g.f. cos(x)/cos(tanh(x)), even powers only.
[ "1", "0", "-8", "56", "512", "-54912", "2590336", "-69311488", "-3936710656", "914002857984", "-81770855727104", "-2175764106870784", "2405710131432685568", "-359158536158603378688", "-106865524988327138951168" ]
[ "sign" ]
17
0
3
[ "A009107", "A009297" ]
null
R. H. Hardin
2018-07-26T08:04:52
oeisdata/seq/A009/A009107.seq
878e644d104ce22aada832701ddcc577
A009108
Expansion of e.g.f. cos(x)/cosh(log(1+x)).
[ "1", "0", "-2", "3", "1", "-30", "164", "-525", "-391", "22428", "-206686", "1039995", "1161337", "-96216978", "1241356024", "-8517557685", "-12681799919", "1373978443800", "-22791296600794", "198084321525267", "368659923645521", "-49339565916861990" ]
[ "sign", "easy" ]
20
0
3
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009108.seq
88609b96a15bd7a3e6732282be5a21fd
A009109
Expansion of e.g.f. cos(x)/cosh(sin(x)), even powers only.
[ "1", "-2", "16", "-328", "12160", "-721280", "62638720", "-7495723264", "1182630301696", "-237887012458496", "59422015832915968", "-18045969534514167808", "6548012482760106213376", "-2797775464269494922051584" ]
[ "sign" ]
19
0
2
null
null
R. H. Hardin
2018-07-26T08:04:59
oeisdata/seq/A009/A009109.seq
3638413419b6efdbcc2b5816739839b8
A009110
Expansion of e.g.f. cos(x)/cosh(tan(x)), even powers only.
[ "1", "-2", "4", "32", "400", "-3680", "-719168", "-45313024", "-1201882880", "190738937344", "41876315935744", "3729103532367872", "-442609357053390848", "-294584246423093633024", "-75554765797484141625344", "-7698772402123265223688192", "3712165683571701387680088064" ]
[ "sign" ]
18
0
2
null
null
R. H. Hardin
2018-07-26T08:05:05
oeisdata/seq/A009/A009110.seq
d2e361ea772f4d32607269ed7ff56f31
A009111
List of ordered areas of Pythagorean triangles.
[ "6", "24", "30", "54", "60", "84", "96", "120", "150", "180", "210", "210", "216", "240", "270", "294", "330", "336", "384", "480", "486", "504", "540", "546", "600", "630", "720", "726", "750", "756", "840", "840", "840", "864", "924", "960", "990", "1014", "1080", "1176", "1224", "1320", "1320", "1344", "1350", "1386", "1470", "1500", "1536", "1560", "1620" ]
[ "nonn" ]
53
1
1
[ "A009111", "A009112", "A024365" ]
null
David W. Wilson
2025-03-12T21:27:08
oeisdata/seq/A009/A009111.seq
bca2333aae6f0f644459af3c14c21eec
A009112
Areas of Pythagorean triangles: numbers which can be the area of a right triangle with integer sides.
[ "6", "24", "30", "54", "60", "84", "96", "120", "150", "180", "210", "216", "240", "270", "294", "330", "336", "384", "480", "486", "504", "540", "546", "600", "630", "720", "726", "750", "756", "840", "864", "924", "960", "990", "1014", "1080", "1176", "1224", "1320", "1344", "1350", "1386", "1470", "1500", "1536", "1560", "1620", "1710", "1716", "1734", "1890" ]
[ "nonn", "easy" ]
86
1
1
[ "A009111", "A009112", "A009127", "A024365", "A073120", "A177021", "A256418" ]
null
David W. Wilson
2025-01-05T19:51:34
oeisdata/seq/A009/A009112.seq
def6e177e32fc5156762b4c7f966a609
A009113
Expansion of e.g.f. cos(x)/exp(sinh(x)).
[ "1", "-1", "0", "1", "0", "3", "-24", "61", "-256", "1383", "-5632", "28345", "-156032", "808299", "-4761600", "28955317", "-178225152", "1188919631", "-8081772544", "56978370417", "-422364381184", "3196912985683", "-25184814366720", "205147130407981", "-1713906141986816" ]
[ "sign", "easy" ]
16
0
6
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009113.seq
4e14b774c684e50e1f0a103ddb15841c
A009114
Expansion of e.g.f. cos(x)/exp(tan(x)).
[ "1", "-1", "0", "0", "4", "-12", "56", "-280", "1744", "-11536", "86208", "-703296", "6199744", "-59653440", "608357504", "-6715007104", "77889982720", "-967972497664", "12588540708864", "-173764741920768", "2503565961032704", "-37986612815698944" ]
[ "sign", "easy" ]
19
0
5
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009114.seq
c21ca35e51f36448d1e26c974e0bd0de
A009115
Expansion of e.g.f. cos(x)/exp(tanh(x)).
[ "1", "-1", "0", "4", "-12", "-12", "216", "-296", "-5296", "25200", "168128", "-1885952", "-5391680", "163728576", "-38412672", "-16916558720", "61881368832", "2050105730816", "-16576603568128", "-282656394482688", "4120672559178752", "42100913802486784" ]
[ "sign", "easy" ]
16
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009115.seq
f55abcc818f0db5fabedea9a71a4a208
A009116
Expansion of e.g.f. cos(x) / exp(x).
[ "1", "-1", "0", "2", "-4", "4", "0", "-8", "16", "-16", "0", "32", "-64", "64", "0", "-128", "256", "-256", "0", "512", "-1024", "1024", "0", "-2048", "4096", "-4096", "0", "8192", "-16384", "16384", "0", "-32768", "65536", "-65536", "0", "131072", "-262144", "262144", "0", "-524288", "1048576", "-1048576", "0", "2097152", "-4194304" ]
[ "sign", "easy", "nice" ]
111
0
4
[ "A009116", "A009545", "A016116", "A066321", "A075553", "A090132", "A098158", "A099087", "A104597", "A146559", "A271472" ]
null
R. H. Hardin
2023-12-30T11:01:45
oeisdata/seq/A009/A009116.seq
01db8d9c6b9c4897980512b6fe8e20db
A009117
Expansion of e.g.f.: 1/2 + exp(-4*x)/2.
[ "1", "-2", "8", "-32", "128", "-512", "2048", "-8192", "32768", "-131072", "524288", "-2097152", "8388608", "-33554432", "134217728", "-536870912", "2147483648", "-8589934592", "34359738368", "-137438953472", "549755813888", "-2199023255552", "8796093022208", "-35184372088832", "140737488355328", "-562949953421312" ]
[ "sign", "easy" ]
59
0
2
[ "A004171", "A009117" ]
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009117.seq
b9912c982aebdc663cf53da8393144d0
A009118
Expansion of e.g.f. cos(x/cos(x)) (even powers only).
[ "1", "-1", "-11", "-181", "-3863", "-66121", "4478365", "1211701763", "226423491793", "43068302925551", "8876725117679941", "1997577117130009403", "483811389670392875449", "121594250947356501211559", "28960468994349845642813677" ]
[ "sign" ]
20
0
3
null
null
R. H. Hardin
2018-07-26T03:21:56
oeisdata/seq/A009/A009118.seq
c475e588160ad6ccf60c41f952bd089a
A009119
Expansion of e.g.f. cos(x/cosh(x)) (even powers only).
[ "1", "-1", "13", "-301", "11705", "-698521", "59340997", "-6782462597", "1000434618609", "-184576848771889", "41577074746699261", "-11216502744649033437", "3567416307426404300713", "-1320192785381894987925961", "562163981454375064332029365", "-272809563505907130928868599861" ]
[ "sign" ]
20
0
3
null
null
R. H. Hardin
2018-07-26T03:43:03
oeisdata/seq/A009/A009119.seq
4d6c8d0827ee5c74ba9c4c64fe3e5cfc
A009120
a(n) = (4n)!/(2n)!.
[ "1", "12", "1680", "665280", "518918400", "670442572800", "1295295050649600", "3497296636753920000", "12576278705767096320000", "58102407620643984998400000", "335367096786357081410764800000", "2365008766537390138108713369600000", "20007974164906320568399715106816000000" ]
[ "nonn", "easy" ]
50
0
2
[ "A001813", "A009120", "A101485" ]
null
R. H. Hardin
2023-01-08T02:40:17
oeisdata/seq/A009/A009120.seq
a86fcb03c88d12377580786240651d08
A009121
Expansion of e.g.f. cosh(exp(x)*x).
[ "1", "0", "1", "6", "25", "100", "481", "2954", "20721", "151848", "1146721", "9111982", "77652169", "710421452", "6891125697", "69961213170", "738718169569", "8108554524112", "92647353941569", "1101958783026134", "13616813607795321", "174287243264606388", "2304515271134124577", "31424734896799742170" ]
[ "nonn", "easy" ]
27
0
4
[ "A000248", "A009017", "A009121", "A009448", "A009565", "A009635", "A009768" ]
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009121.seq
d617d12faa2a701babbd77e6ee353570
A009122
Expansion of e.g.f. cosh(log(1+log(1+x))).
[ "1", "0", "1", "-6", "41", "-335", "3229", "-36036", "457932", "-6534384", "103499016", "-1802302128", "34227784920", "-704076488232", "15595687319640", "-370108332316992", "9368461983616128", "-251958336139856448", "7174771808983995456" ]
[ "sign", "easy" ]
19
0
4
[ "A009122", "A052864" ]
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009122.seq
f0322d14a2e8e50589f0a21d3253d3cf
A009123
Expansion of e.g.f.: cosh(log(1+sin(x))).
[ "1", "0", "1", "-3", "8", "-30", "136", "-693", "3968", "-25260", "176896", "-1351383", "11184128", "-99680490", "951878656", "-9695756073", "104932671488", "-1202439837720", "14544442556416", "-185185594118763", "2475749026562048", "-34674437196568950" ]
[ "sign", "easy" ]
28
0
4
[ "A000111", "A009123" ]
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009123.seq
58311f317e94205f4cb00cbe5a090d71
A009124
Expansion of e.g.f. cosh(log(1+sinh(x))).
[ "1", "0", "1", "-3", "16", "-90", "616", "-4893", "44416", "-453540", "5145856", "-64222983", "874402816", "-12897183390", "204862698496", "-3486535686273", "63292764553216", "-1220795601029640", "24931903045697536", "-537463528325234763" ]
[ "sign", "easy" ]
20
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009124.seq
64c12a6c62e7057328cf39a1a45aff0b
A009125
Expansion of e.g.f. cosh(log(1+tan(x))).
[ "1", "0", "1", "-3", "20", "-120", "976", "-8568", "88640", "-1011840", "12933376", "-180964608", "2767631360", "-45799004160", "816582578176", "-15594628021248", "317710534983680", "-6876762625966080", "157606194409701376", "-3812723805066559488" ]
[ "sign", "easy" ]
19
0
4
null
null
R. H. Hardin
2023-03-08T12:08:39
oeisdata/seq/A009/A009125.seq
4f23673f48d5bcc74510b6aab548d5c4
A009126
Expansion of e.g.f. cosh(log(1+tanh(x))).
[ "1", "0", "1", "-3", "4", "0", "16", "-168", "64", "3840", "256", "-177408", "1024", "11182080", "4096", "-951886848", "16384", "104932638720", "65536", "-14544442687488", "262144", "2475749026037760", "1048576", "-507711943255523328", "4194304", "123460740095095603200", "16777216" ]
[ "sign", "easy" ]
21
0
4
[ "A009126", "A009570" ]
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009126.seq
a32cb93411268b2f5e4aaf9ad7be35c3
A009127
Area of more than one Pythagorean triangle.
[ "210", "840", "1320", "1890", "2730", "3360", "4914", "5250", "5280", "7560", "7980", "10290", "10920", "11880", "13440", "17010", "18480", "19656", "21000", "21120", "24570", "25410", "29400", "30240", "30600", "31920", "32130", "33000", "34650", "35490", "41160", "41580", "43680", "44226", "45144", "47250", "47520", "50490" ]
[ "nonn" ]
13
1
1
[ "A009111", "A009127" ]
null
David W. Wilson
2017-08-16T06:56:29
oeisdata/seq/A009/A009127.seq
6cb4b9066276e6abf42a9b9a43f1e8d2
A009128
Expansion of e.g.f. cosh(log(1+x))*cos(x).
[ "1", "0", "0", "-3", "7", "-30", "194", "-1365", "10893", "-98028", "980324", "-10783575", "129402835", "-1682236842", "23551315878", "-353269738185", "5652315810841", "-96089368784280", "1729608638117192", "-32862564124226667", "657251282484533151" ]
[ "sign", "easy" ]
18
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009128.seq
e9b582b7a8518cc857cc1bec13a60b17
A009129
Perimeter of more than one Pythagorean triangle.
[ "60", "84", "90", "120", "132", "144", "168", "180", "210", "240", "252", "264", "270", "280", "288", "300", "312", "330", "336", "360", "390", "396", "408", "420", "432", "440", "450", "456", "462", "468", "480", "504", "510", "520", "528", "540", "546", "552", "560", "570", "576", "588", "600", "612", "616", "624", "630", "660", "672", "680", "684", "690", "700", "720" ]
[ "nonn" ]
10
1
1
[ "A009129", "A010814" ]
null
David W. Wilson
2018-02-03T21:32:33
oeisdata/seq/A009/A009129.seq
73a7cbabb3a2870509cfe8a54a3b54a9
A009130
Expansion of e.g.f. cosh(log(1+x))/cos(x).
[ "1", "0", "2", "-3", "23", "-90", "676", "-4305", "37533", "-325332", "3366166", "-36472095", "443702291", "-5732993838", "80707226328", "-1207617980205", "19365202513145", "-328878787017000", "5925189947339626", "-112532916285619515", "2251485624038961615" ]
[ "sign", "easy" ]
19
0
3
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009130.seq
1a5779fed82669eac693b2739e6a0927
A009131
Expansion of e.g.f. cosh(log(1+x))/cosh(x).
[ "1", "0", "0", "-3", "11", "-30", "194", "-1785", "13957", "-113148", "1143284", "-13131855", "156950639", "-2005222362", "28119703702", "-424785970245", "6792043718345", "-115135087505400", "2072993596779944", "-39432571052652315", "788564865102950035" ]
[ "sign", "easy" ]
17
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009131.seq
4a8caa39d9dcc3489b2de99d1771aff1
A009132
Expansion of e.g.f. cosh(log(1+x))/exp(x).
[ "1", "-1", "2", "-7", "31", "-161", "976", "-6847", "54797", "-493201", "4932046", "-54252551", "651030667", "-8463398737", "118487582396", "-1777313736031", "28437019776601", "-483429336202337", "8701728051642202", "-165332832981201991", "3306656659624039991" ]
[ "sign", "easy" ]
24
0
3
[ "A009132", "A009578" ]
null
R. H. Hardin
2024-12-29T21:41:14
oeisdata/seq/A009/A009132.seq
a3c1ee910dc9fa34dba6f525c7e90d4d
A009133
Expansion of e.g.f. cosh(log(1+x)*cos(x)).
[ "1", "0", "1", "-3", "0", "0", "90", "-420", "3192", "-36792", "344640", "-3424080", "40458792", "-515760960", "6995451736", "-102430659240", "1603858275328", "-26656736919808", "469564051796928", "-8742335523613056", "171465068564306560", "-3533692765499863680" ]
[ "sign", "easy" ]
17
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009133.seq
d2b6c376bc69cd938166e6019af3e76e
A009134
Expansion of cosh(log(1+x)*cosh(x)).
[ "1", "0", "1", "-3", "24", "-120", "870", "-6300", "55048", "-527688", "5684640", "-66667920", "850501608", "-11675938560", "171892670040", "-2700017534760", "45091783981312", "-797817318871552", "14909393380875840", "-293452734825051264" ]
[ "sign", "easy" ]
17
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009134.seq
a9a83269516c0a5efcb4c074fcb16ff8
A009135
Expansion of e.g.f. cosh(log(1+x)*exp(x)).
[ "1", "0", "1", "3", "12", "30", "180", "490", "5600", "8064", "276360", "-575872", "22950576", "-166106512", "3194871680", "-38456524080", "663548916992", "-10330038449792", "186243968575488", "-3385894106098944", "66478140305126272", "-1354838641265098752" ]
[ "sign", "easy" ]
23
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009135.seq
e9fc4d4b49beb3e8b7478bd2ea49b309
A009136
Expansion of e.g.f. cosh(x*log(1+x)).
[ "1", "0", "0", "0", "12", "-60", "330", "-2100", "17024", "-157248", "1604520", "-17875440", "216589032", "-2838607200", "40020882720", "-603994154400", "9715670780160", "-165944432465280", "2999458158459840", "-57201489673372800", "1147839380364481920" ]
[ "sign", "easy" ]
22
0
5
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009136.seq
c0135277d8188af021aa3eb83924557a
A009137
Expansion of e.g.f. cosh(log(1+x)/cos(x)).
[ "1", "0", "1", "-3", "24", "-120", "990", "-7140", "69048", "-658728", "7542960", "-89216160", "1191378408", "-16691737920", "255303337016", "-4111553595240", "70932973452032", "-1287129875516672", "24738396315075648", "-498729120183554688" ]
[ "sign", "easy" ]
20
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009137.seq
cfa06efd45653362bb1a3b68ddac2514
A009138
Expansion of e.g.f.: cosh(log(1+x)/cosh(x)).
[ "1", "0", "1", "-3", "0", "0", "210", "-1260", "3752", "-46872", "690960", "-6013920", "58389672", "-895065600", "12888358392", "-168411308520", "2621915506688", "-47022586623488", "824126273574336", "-14767693271763840", "293589445235224960" ]
[ "sign", "easy" ]
26
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009138.seq
a7732452e93c9ce5a602a4c9a31e78f1
A009139
Expansion of e.g.f. cosh(log(1+x)/exp(x)).
[ "1", "0", "1", "-9", "60", "-390", "2820", "-24010", "238336", "-2659104", "32417160", "-426027008", "6004088112", "-90491148176", "1454386367616", "-24843370627920", "449435283828992", "-8582294948325760", "172476215457600000", "-3638420414864043264" ]
[ "sign", "easy" ]
20
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009139.seq
051f719fd30fcb4bcd1c4f40cffdaa99
A009140
Expansion of e.g.f. cosh(log(1+x)^2).
[ "1", "0", "0", "0", "12", "-120", "1020", "-8820", "82908", "-867888", "10145760", "-131406000", "1864232832", "-28656815616", "473108471472", "-8332064722800", "155724385537488", "-3076215029701248", "64018830395437056", "-1399676595110345088" ]
[ "sign", "easy" ]
18
0
5
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009140.seq
3063a7cd05413d0e5add1e5111823bb7
A009141
Expansion of e.g.f. cosh(sin(log(1+x))).
[ "1", "0", "1", "-3", "8", "-20", "16", "504", "-7988", "98064", "-1148444", "13529780", "-163362904", "2034844032", "-26171589352", "346739305080", "-4707342441904", "64916998981504", "-896227413179888", "12056914630083024", "-148732421110480064" ]
[ "sign", "easy" ]
18
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009141.seq
3ca24b07cc04d46c3d75cb43bb4699a4
A009142
Expansion of e.g.f. cosh(sin(sin(x))), even powers only.
[ "1", "1", "-7", "73", "-687", "-19471", "2839561", "-260138759", "22560194593", "-1856685484703", "115492830956953", "5211807618131753", "-4918276086306813839", "1664523472944706933841", "-477486870436056568353623" ]
[ "sign" ]
20
0
3
null
null
R. H. Hardin
2018-07-31T02:39:57
oeisdata/seq/A009/A009142.seq
68cea2c06511f6708b27de83cc738bf3
A009143
Expansion of e.g.f. cosh(sin(tan(x))), even powers only.
[ "1", "1", "5", "13", "-2199", "-218311", "-20057555", "-1933691003", "-181405779887", "-10159446470927", "2835996855537109", "1885678632476987261", "824453354251620790969", "331368644928193180404521", "128606636719913204236509949" ]
[ "sign" ]
20
0
3
null
null
R. H. Hardin
2018-07-31T02:39:46
oeisdata/seq/A009/A009143.seq
ba99cbc707e5ae89ff4fcb3b803f55a0
A009144
Expansion of cosh(sin(x))/cos(x).
[ "1", "2", "8", "88", "2176", "78080", "4159616", "307882240", "29920681984", "3710767394816", "571523842998272", "107010484096565248", "23940179383147724800", "6306683724617339961344", "1932337463823712544620544" ]
[ "nonn" ]
11
0
2
null
null
R. H. Hardin
2015-01-22T12:34:44
oeisdata/seq/A009/A009144.seq
cbc0a0ae1b879f6585b55260d0deb106
A009145
Expansion of e.g.f.: cosh(sin(x))/exp(x).
[ "1", "-1", "2", "-4", "4", "4", "-32", "104", "-48", "-1360", "5600", "-1024", "-85568", "494272", "-533504", "-13790848", "85827840", "68726528", "-3149702656", "15167771648", "27282224128", "-993154165760", "5424499154944", "28626523621376", "-496815684169728", "1093475947065344" ]
[ "sign", "easy" ]
13
0
3
null
null
R. H. Hardin
2020-06-09T18:30:06
oeisdata/seq/A009/A009145.seq
a7ab1b6147b8265028cce7249ddaaf37
A009146
Expansion of cosh(sin(x)*cos(x)).
[ "1", "1", "-15", "177", "1057", "-245471", "15691665", "-608056239", "-20287425215", "8821231566145", "-1376333505095631", "139148719952772849", "-994319439549289631", "-4366129925254794998687", "1524646116370009191174609" ]
[ "sign" ]
12
0
3
null
null
R. H. Hardin
2017-04-01T11:50:21
oeisdata/seq/A009/A009146.seq
0ed813e96ee41a9b97bf91b08bbc0d51
A009147
Expansion of e.g.f.: cosh(sin(x)*exp(x)).
[ "1", "0", "1", "6", "21", "60", "237", "1498", "9289", "46872", "208249", "1096590", "7953693", "57151380", "296264997", "707086882", "-2635164911", "-25223244624", "-123580612751", "-4185669625194", "-97178084153691", "-1235239023971988", "-9092858617394211" ]
[ "sign", "easy" ]
18
0
4
null
null
R. H. Hardin
2022-07-02T15:49:10
oeisdata/seq/A009/A009147.seq
838584b7821d844e9424717153007e51
A009148
Expansion of cosh(sin(x)*log(1+x)).
[ "1", "0", "0", "0", "12", "-60", "210", "-1260", "11760", "-114912", "1111560", "-11676720", "138570696", "-1799232864", "25005472128", "-371229549600", "5885388887040", "-99270313446784", "1773606197591232", "-33452898176207232", "664355584657373312" ]
[ "sign", "easy" ]
12
0
5
null
null
R. H. Hardin
2025-03-10T16:38:30
oeisdata/seq/A009/A009148.seq
1d040e6030dd0e5f1b68b981f2e21964
A009149
Expansion of e.g.f. cosh(sin(x)*x), even powers only.
[ "1", "0", "12", "-120", "2576", "-106560", "4690752", "-251957888", "17894058240", "-1518819416064", "147193120578560", "-16536681255671808", "2144498299945291776", "-313806765843863552000", "51199709803672550916096" ]
[ "sign" ]
15
0
3
null
null
R. H. Hardin
2014-02-09T04:06:58
oeisdata/seq/A009/A009149.seq
98ae050b52cfaa677bc9c16fe1a547d8
A009150
Expansion of e.g.f. cosh(sin(x)^2) (even coefficients).
[ "1", "0", "12", "-240", "5712", "-266880", "18566592", "-1488963840", "141287377152", "-16736203345920", "2412897423240192", "-402658140395089920", "76287123858146906112", "-16430034737688309104640", "4011640516519571786022912", "-1097783068806961397511290880" ]
[ "sign" ]
18
0
3
null
null
R. H. Hardin
2017-04-01T11:49:22
oeisdata/seq/A009/A009150.seq
f2e4e690c7c4291d89bed7350193d7fb
A009151
Expansion of cosh(sinh(log(1+x))).
[ "1", "0", "1", "-3", "16", "-100", "736", "-6216", "59284", "-630288", "7391836", "-94796020", "1319653336", "-19816887168", "319274039176", "-5492805409560", "100490908021456", "-1947909828835456", "39875223857927824", "-859529863811898288" ]
[ "sign", "easy" ]
10
0
4
null
null
R. H. Hardin
2015-06-21T21:53:14
oeisdata/seq/A009/A009151.seq
dffa2a622489299e7581e3599f38543c
A009152
Expansion of e.g.f. cosh(sinh(x))/exp(x).
[ "1", "-1", "2", "-4", "12", "-36", "128", "-456", "1872", "-7888", "37600", "-184064", "990784", "-5444544", "32333824", "-195982208", "1272660224", "-8441139456", "59527313920", "-428299217920", "3252626013184", "-25165446157312", "204354574172160", "-1689266143553536" ]
[ "sign", "easy" ]
15
0
3
null
null
R. H. Hardin
2019-03-31T07:19:16
oeisdata/seq/A009/A009152.seq
51d57d4e1c92278829de6efcc12cb04b
A009153
Expansion of e.g.f. cosh(sinh(x)*exp(x)).
[ "1", "0", "1", "6", "29", "140", "757", "4858", "36409", "302520", "2681769", "25018510", "245905365", "2559272196", "28264854685", "330408571202", "4065526003313", "52349977261040", "702393407898705", "9795673312888214", "141820637175889805" ]
[ "nonn", "easy" ]
54
0
4
[ "A009153", "A009599", "A065143" ]
null
R. H. Hardin
2017-10-07T02:35:08
oeisdata/seq/A009/A009153.seq
3cf8dd74778454101bd42be5f9d00c67
A009154
E.g.f.: Expansion of cosh(sinh(x)*log(1+x)).
[ "1", "0", "0", "0", "12", "-60", "450", "-2940", "24080", "-215712", "2245320", "-25552560", "318861576", "-4280157024", "61675886272", "-948295464480", "15514105784320", "-269094947517824", "4934169151898304", "-95367032452388736", "1937946889478705792" ]
[ "sign", "easy" ]
14
0
5
null
null
R. H. Hardin
2015-06-21T21:53:05
oeisdata/seq/A009/A009154.seq
a05ddf8186eb9b4a055a7fcdf6d98c2d
A009155
Expansion of cosh(sinh(x)*sin(x)).
[ "1", "12", "1232", "-187968", "-743941888", "1067281001472", "11143403147251712", "-105243085074533203968", "-981733215490919764000768", "52944309012028493003521523712", "-256259148179480526283367831830528" ]
[ "sign" ]
10
0
2
null
null
R. H. Hardin
2017-04-01T07:24:15
oeisdata/seq/A009/A009155.seq
84ba009183c9f982a1b723419b141d3b
A009156
Expansion of e.g.f.: cosh(tan(log(1+x))).
[ "1", "0", "1", "-3", "20", "-140", "1216", "-12096", "137080", "-1737504", "24368656", "-374527120", "6259083896", "-112992788688", "2191121957480", "-45420491782680", "1002232901602496", "-23453004823018496", "580102806342112960" ]
[ "sign", "easy" ]
12
0
4
null
null
R. H. Hardin
2015-06-21T21:52:53
oeisdata/seq/A009/A009156.seq
321c1b3e4a7f799f7b9a6ef4627f1798
A009157
Expansion of cosh(tan(sin(x))).
[ "1", "1", "5", "13", "-855", "-38791", "-747539", "59637061", "9421489105", "573991066225", "-49290541346219", "-20481513828195331", "-2616109089676671623", "259051585957836649961", "218489079668015355338557", "45857020942077467007882293", "-6052305324824723639484616287" ]
[ "sign" ]
15
0
3
null
null
R. H. Hardin
2017-04-01T11:48:43
oeisdata/seq/A009/A009157.seq
cc53cb20f7a147883f244ad781e22a3e
A009158
Expansion of cosh(tan(tan(x))).
[ "1", "1", "17", "673", "48033", "5387009", "871869745", "192177458593", "55316788832065", "20139680768683777", "9044546204411462737", "4909707244721993221025", "3168104630099094560839393", "2396238201505538217521920001" ]
[ "nonn" ]
10
0
3
null
null
R. H. Hardin
2024-08-18T12:46:36
oeisdata/seq/A009/A009158.seq
e491e03bc27c7642c9a9bd95e9b5a747
A009159
Expansion of cosh(tan(x))*cos(x).
[ "1", "0", "4", "56", "1744", "86208", "6199744", "608357504", "77889982720", "12588540708864", "2503565961032704", "600347512023062528", "170721835772956659712", "56780394898390577528832", "21828678118361789793746944" ]
[ "nonn" ]
11
0
3
null
null
R. H. Hardin
2019-07-28T19:20:32
oeisdata/seq/A009/A009159.seq
4e446734cd3fb2c796b9debd9b22d599
A009160
Expansion of cosh(tan(x))/cos(x).
[ "1", "2", "20", "448", "17296", "1013600", "83547584", "9196867072", "1301697829120", "230093807905280", "49636887216382976", "12825384465418534912", "3908078275606800338944", "1386160615200497825275904" ]
[ "nonn" ]
8
0
2
null
null
R. H. Hardin
2014-01-27T09:12:45
oeisdata/seq/A009/A009160.seq
dc4662749adecddb91bb510081107770
A009161
Expansion of cosh(tan(x))/exp(x).
[ "1", "-1", "2", "-4", "16", "-56", "328", "-1576", "11712", "-70912", "638720", "-4668544", "49459840", "-423673472", "5159926528", "-50674728448", "697030680576", "-7717401038848", "118233272496128", "-1456461190426624", "24578235697610752", "-333308651379949568" ]
[ "sign", "easy" ]
15
0
3
null
null
R. H. Hardin
2014-04-09T04:27:26
oeisdata/seq/A009/A009161.seq
1cd350263d1fb96e52744fd721926821
A009162
Expansion of cosh(tan(x).exp(x)).
[ "1", "0", "1", "6", "33", "180", "1137", "8218", "68929", "640584", "6534049", "71605710", "842179041", "10543617084", "140430103569", "1979476257442", "29478515793025", "461911114620432", "7600066231728193", "130898815536828438" ]
[ "nonn", "easy" ]
8
0
4
null
null
R. H. Hardin
2014-01-27T09:12:45
oeisdata/seq/A009/A009162.seq
89c09246ec5fc9fa05887a4fa6bf27a4
A009163
Expansion of e.g.f.: cosh(tan(x)*log(1+x)).
[ "1", "0", "0", "0", "12", "-60", "570", "-3780", "36960", "-326592", "3712200", "-41836080", "554861736", "-7563345504", "114963916704", "-1819859452320", "31173297642240", "-558346710891904", "10642982507666880", "-212150797420894848", "4456607540110934912" ]
[ "sign", "easy" ]
12
0
5
null
null
R. H. Hardin
2022-07-14T17:07:45
oeisdata/seq/A009/A009163.seq
a3e449e57687fd57c532eb9bd9ecab7f
A009164
Expansion of cosh(tan(x)*sin(x)).
[ "1", "0", "12", "120", "5712", "277440", "22051392", "2264545920", "305454289152", "51584380815360", "10690872186043392", "2662785210401986560", "784469273871443546112", "269661019173783209656320" ]
[ "nonn" ]
9
0
3
null
null
R. H. Hardin
2014-01-27T09:12:45
oeisdata/seq/A009/A009164.seq
baa0c87a72c29c14e7b11df47b43faeb
A009165
Expansion of cosh(tan(x)*sinh(x)).
[ "1", "0", "12", "360", "14672", "947520", "89973312", "11518066560", "1887213285632", "383583690823680", "94596308487109632", "27811060234433710080", "9605125245736932134912", "3848453455438561596456960" ]
[ "nonn" ]
11
0
3
null
null
R. H. Hardin
2020-08-14T14:39:33
oeisdata/seq/A009/A009165.seq
372b419bfa7037f6a133971968e2325d
A009166
Expansion of cosh(tan(x)*x).
[ "1", "0", "12", "240", "9296", "558720", "47965632", "5537249536", "823842474240", "153119256219648", "34710583399132160", "9416311849673895936", "3009741915237844832256", "1118809461121375449088000" ]
[ "nonn" ]
12
0
3
null
null
R. H. Hardin
2015-01-24T08:09:37
oeisdata/seq/A009/A009166.seq
e2db1c68f0df240aa3f6adb8693ad5d7
A009167
Expansion of cosh(tan(x)/cos(x)).
[ "1", "1", "21", "717", "38857", "3158329", "363525789", "56250039237", "11210469917713", "2783865475754737", "840008000833503141", "302092032859131150141", "127513257396264637784281", "62381091849825754078253353" ]
[ "nonn" ]
10
0
3
null
null
R. H. Hardin
2015-02-11T12:23:06
oeisdata/seq/A009/A009167.seq
e42fb58abc8d52257018ebff1e9c3c53
A009168
Expansion of cosh(tan(x)^2).
[ "1", "0", "12", "480", "25872", "2031360", "227781312", "34846855680", "6932161765632", "1724433365360640", "521307469175442432", "187630895361738301440", "79180079598904589094912", "38701262478049196612321280" ]
[ "nonn" ]
8
0
3
null
null
R. H. Hardin
2014-01-27T09:12:45
oeisdata/seq/A009/A009168.seq
5e16505db0a44d7a3f7a492be6c1e44f
A009169
Expansion of cosh(tanh(log(1+x))).
[ "1", "0", "1", "-3", "4", "20", "-224", "1344", "-5144", "-4320", "356896", "-4755520", "42368536", "-207434448", "-1593929336", "61487349000", "-997231605824", "9976381236224", "-16539522000704", "-1929601048449600", "51992648244966016", "-800205465246136320" ]
[ "sign", "easy" ]
10
0
4
null
null
R. H. Hardin
2015-06-21T21:52:41
oeisdata/seq/A009/A009169.seq
31752113463b06b77bdde4e1398a93d8
A009170
Expansion of cosh(tanh(x))/exp(x).
[ "1", "-1", "2", "-4", "0", "24", "8", "-456", "192", "11264", "-20480", "-289664", "1837696", "-3000960", "-187743488", "2697206272", "22698672128", "-625547980800", "-3236847570944", "138214081974272", "536307107184640", "-32824743592198144", "-101121059849109504" ]
[ "sign", "easy" ]
11
0
3
null
null
R. H. Hardin
2017-04-01T11:48:27
oeisdata/seq/A009/A009170.seq
79b7d0f0de766d0828edd292a1e0f1c9
A009171
Expansion of cosh(tanh(x)*exp(x)).
[ "1", "0", "1", "6", "17", "20", "97", "1498", "7009", "-8952", "-44991", "2641870", "16678257", "-147810468", "-1072851167", "22562632802", "182236444097", "-3111217127536", "-28067216775039", "608465230881302", "6014702853818321", "-136728540813908444" ]
[ "sign", "easy" ]
11
0
4
null
null
R. H. Hardin
2017-04-01T11:48:11
oeisdata/seq/A009/A009171.seq
e7b565f47bb82a4d339aac34c3b1f1d7
A009172
Expansion of e.g.f.: cosh(tanh(x)*log(1+x)).
[ "1", "0", "0", "0", "12", "-60", "90", "-420", "12320", "-124992", "753480", "-6481200", "110644776", "-1613081184", "18917874976", "-250425171360", "4359533351680", "-78311204695424", "1329852024578496", "-23869209971687040", "483284209880289152" ]
[ "sign", "easy" ]
13
0
5
null
null
R. H. Hardin
2015-06-21T21:52:22
oeisdata/seq/A009/A009172.seq
b96a6e1ccaad291aedf7232fafd4bd73
A009173
Expansion of cosh(tanh(x)*tan(x)).
[ "1", "12", "7952", "31111872", "414147567872", "13936708915940352", "987956358173680013312", "130572314003924554412900352", "29485421729721202391180048924672", "10655360784935131422152244665663619072" ]
[ "nonn" ]
11
0
2
null
null
R. H. Hardin
2020-08-19T12:23:15
oeisdata/seq/A009/A009173.seq
e38889c524cba79ca460b3ed888c8941
A009174
Expansion of e.g.f.: cosh(x)*cos(log(1+x)).
[ "1", "0", "0", "3", "-15", "70", "-354", "1995", "-12667", "89892", "-705244", "6042575", "-55837075", "548985138", "-5650236630", "59493168735", "-615581655639", "5683518687560", "-30016869620472", "-587400084741573", "31322604753002761", "-1006072267431660450" ]
[ "sign", "easy" ]
13
0
4
null
null
R. H. Hardin
2015-06-21T21:52:16
oeisdata/seq/A009/A009174.seq
a72093f2a87c24f9786f5fb2d3203c0d
A009175
Expansion of cosh(x)*cos(sin(x)).
[ "1", "0", "0", "24", "-256", "5632", "-156032", "4761600", "-178225152", "8081772544", "-422364381184", "25184814366720", "-1713906141986816", "131755307615387648", "-11304870125221445632", "1075236678976585072640", "-112837158484808719925248" ]
[ "sign" ]
14
0
4
null
null
R. H. Hardin
2024-12-15T15:18:23
oeisdata/seq/A009/A009175.seq
4778067b7a50ced4be3e9f7a19f8ab69
A009176
Expansion of e.g.f.: cosh(x)*cos(tan(x)).
[ "1", "0", "-12", "-216", "-5296", "-168128", "-5391680", "38412672", "61881368832", "16576603568128", "4120672559178752", "1085659391947229184", "313198080458495610880", "99633528964523733598208", "34860299883730859703910400" ]
[ "sign" ]
16
0
3
null
null
R. H. Hardin
2023-03-17T12:14:37
oeisdata/seq/A009/A009176.seq
a12b0155cd7d630d839c7bcb50b55ef8
A009177
Numbers that are the hypotenuses of more than one Pythagorean triangle.
[ "25", "50", "65", "75", "85", "100", "125", "130", "145", "150", "169", "170", "175", "185", "195", "200", "205", "221", "225", "250", "255", "260", "265", "275", "289", "290", "300", "305", "325", "338", "340", "350", "365", "370", "375", "377", "390", "400", "410", "425", "435", "442", "445", "450", "455", "475", "481", "485", "493", "500", "505", "507", "510", "520", "525" ]
[ "nonn" ]
43
1
1
[ "A004431", "A009000", "A009177", "A118882", "A121387" ]
null
David W. Wilson
2025-02-14T08:04:49
oeisdata/seq/A009/A009177.seq
3218a257b6124cf6d6fd3376a551715e
A009178
Expansion of cosh(x)*cosh(log(1+x)).
[ "1", "0", "2", "-3", "19", "-90", "556", "-3885", "31109", "-279972", "2799766", "-30797415", "369569047", "-4804397598", "67261566464", "-1008923496945", "16142775951241", "-274427191171080", "4939689441079594", "-93854099380512267", "1877081987610245531" ]
[ "sign", "easy" ]
18
0
3
null
null
R. H. Hardin
2015-06-21T21:52:08
oeisdata/seq/A009/A009178.seq
4c5d349f3800c745e65dfd350bd16f60
A009179
E.g.f. cosh(x)/(1+x).
[ "1", "-1", "3", "-9", "37", "-185", "1111", "-7777", "62217", "-559953", "5599531", "-61594841", "739138093", "-9608795209", "134523132927", "-2017846993905", "32285551902481", "-548854382342177", "9879378882159187", "-187708198761024553", "3754163975220491061" ]
[ "sign", "easy" ]
39
0
3
[ "A000166", "A000522", "A001540", "A009179", "A009628" ]
null
R. H. Hardin
2023-12-30T10:57:48
oeisdata/seq/A009/A009179.seq
0e95be5b648aea34d40f3b982fbe07f1
A009180
Expansion of cosh(x)/cos(log(1+x)).
[ "1", "0", "2", "-3", "23", "-130", "1016", "-8925", "90369", "-1027332", "12980406", "-180372995", "2734039527", "-44890794078", "793705143908", "-15034678005165", "303761462921921", "-6520477426903400", "148194700045065674", "-3555110881720345347" ]
[ "sign", "easy" ]
13
0
3
null
null
R. H. Hardin
2015-06-21T21:51:49
oeisdata/seq/A009/A009180.seq
78af373f963d78a74a8050d601687695
A009181
Expansion of cosh(x)/cos(sin(x)).
[ "1", "2", "8", "8", "-960", "-22400", "251008", "53882624", "2088660992", "-173107810304", "-34807275798528", "-1238452597522432", "561542864118906880", "119928087297015742464", "-1488492672130035744768", "-6684251211519983379283968", "-1421114720526402152671739904" ]
[ "sign" ]
14
0
2
null
null
R. H. Hardin
2017-04-01T11:47:02
oeisdata/seq/A009/A009181.seq
7baeb80774d7f16bd7ec16cba5aa0fa3
A009182
Expansion of cosh(x)/cos(tan(x)).
[ "1", "2", "20", "608", "34320", "3084640", "405224896", "73292662784", "17468683774208", "5306511481924096", "2001393333656871936", "917626310129679884288", "502654675782900203720704", "324215069803278031144280064" ]
[ "nonn" ]
11
0
2
null
null
R. H. Hardin
2015-01-22T12:42:02
oeisdata/seq/A009/A009182.seq
69baf3f53503da5205edc4fc7396cfd1
A009183
Expansion of e.g.f.: cosh(x)/cosh(log(1+x)).
[ "1", "0", "0", "3", "-11", "30", "-14", "-525", "4593", "-22428", "17596", "1039995", "-13641275", "96216978", "-105681666", "-8517557685", "148962722881", "-1373978443800", "1940315387608", "198084321525267", "-4330346354150859", "49339565916861990", "-85160442362115350" ]
[ "sign", "easy" ]
14
0
4
null
null
R. H. Hardin
2015-06-21T21:51:39
oeisdata/seq/A009/A009183.seq
42e5bc01d43290a80a09b5b8bb22f2ca
A009184
Expansion of e.g.f.: cosh(x)/exp(sin(x)).
[ "1", "-1", "2", "-3", "4", "3", "-32", "105", "-48", "-1081", "5600", "-5643", "-85568", "547467", "-533504", "-12925983", "85827840", "-21466225", "-3149702656", "19155660141", "27282224128", "-1094661097965", "5424499154944", "26420430767577", "-496815684169728", "1642571602653527" ]
[ "sign", "easy" ]
13
0
3
null
null
R. H. Hardin
2017-06-11T18:19:36
oeisdata/seq/A009/A009184.seq
f856050df47ed1412ef8e33725504ab2
A009185
Long leg of more than one Pythagorean triangle.
[ "12", "24", "36", "40", "45", "48", "56", "60", "63", "72", "80", "84", "90", "96", "105", "108", "112", "120", "126", "132", "135", "140", "144", "156", "160", "165", "168", "176", "180", "189", "192", "195", "200", "204", "208", "210", "216", "220", "224", "225", "228", "231", "240", "252", "255", "260", "264", "270", "272", "273", "275", "276", "280", "285", "288", "300", "304" ]
[ "nonn" ]
15
1
1
[ "A009012", "A009185", "A009188", "A020883", "A033942" ]
null
David W. Wilson
2018-04-20T16:43:16
oeisdata/seq/A009/A009185.seq
0f11c0ed4d3485c023effef298fa95f9
A009186
Expansion of e.g.f.: cosh(x)/exp(tan(x)).
[ "1", "-1", "2", "-6", "16", "-72", "328", "-1848", "11712", "-81088", "638720", "-5318016", "49459840", "-483162240", "5159926528", "-57865303296", "697030680576", "-8815813734400", "118233272496128", "-1662921003208704", "24578235697610752", "-380141599264751616", "6139851821419921408" ]
[ "sign", "easy" ]
18
0
3
null
null
R. H. Hardin
2024-12-10T08:58:33
oeisdata/seq/A009/A009186.seq
966665380fe613ce8b4dbc1715c52c30
A009187
Expansion of cosh(x)/exp(tanh(x)).
[ "1", "-1", "2", "-2", "0", "8", "8", "-184", "192", "5568", "-20480", "-231552", "1837696", "11751296", "-187743488", "-596164352", "22698672128", "4342886400", "-3236847570944", "10035384119296", "536307107184640", "-3825733461393408", "-101121059849109504" ]
[ "sign", "easy" ]
11
0
3
null
null
R. H. Hardin
2017-04-01T11:46:29
oeisdata/seq/A009/A009187.seq
05a91466e8a304f61d079e9a489df092
A009188
Short leg of more than one Pythagorean triangle.
[ "9", "12", "15", "16", "18", "20", "21", "24", "25", "27", "28", "30", "32", "33", "35", "36", "39", "40", "42", "44", "45", "48", "49", "50", "51", "52", "54", "55", "56", "57", "60", "63", "64", "65", "66", "68", "69", "70", "72", "75", "76", "77", "78", "80", "81", "84", "85", "87", "88", "90", "91", "92", "93", "95", "96", "98", "99", "100", "102", "104", "105", "108", "110", "111", "112", "114", "115", "116" ]
[ "nonn" ]
48
1
1
[ "A001749", "A009004", "A009188", "A020884", "A046315", "A264828" ]
null
David W. Wilson
2024-10-17T17:41:28
oeisdata/seq/A009/A009188.seq
71d3046c4e9866eaf0f298f2563c48aa
A009189
Expansion of e.g.f.: exp(cos(x)*x).
[ "1", "1", "1", "-2", "-11", "-24", "61", "624", "1737", "-7424", "-88679", "-242560", "2086525", "23499776", "45950997", "-1002251264", "-9763133167", "-2151563264", "705668046769", "5583112077312", "-17356978593659", "-666018502836224", "-3823112141007763", "39230927775531008", "788728947108214489" ]
[ "sign", "easy" ]
33
0
4
[ "A003727", "A009189", "A352252" ]
null
R. H. Hardin
2022-03-26T13:41:04
oeisdata/seq/A009/A009189.seq
d333db2a198a1fd55c39d1e729fabd23
A009190
"2p-twin peaks": a(n) is the least x with lpf(x) = lpf(x + 2p) = p = prime(n) and lpf(y) < p for all x < y < x + 2p, where lpf = least prime factor; a(n) = -1 if no such x exists.
[ "7310131732015251470110369", "2061519317176132799110061", "3756800873017263196139951", "6316254452384500173544921", "14733008374252975993271023", "532045863029111910656094569", "476592878661578285779747459" ]
[ "nonn", "more" ]
59
20
1
[ "A009190", "A020639", "A058989" ]
null
David W. Wilson
2025-02-16T08:32:32
oeisdata/seq/A009/A009190.seq
362957ac0f3c3c1b02a8f3cede7f288a
A009191
a(n) = gcd(n, d(n)), where d(n) is the number of divisors of n (A000005).
[ "1", "2", "1", "1", "1", "2", "1", "4", "3", "2", "1", "6", "1", "2", "1", "1", "1", "6", "1", "2", "1", "2", "1", "8", "1", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "9", "1", "2", "1", "8", "1", "2", "1", "2", "3", "2", "1", "2", "1", "2", "1", "2", "1", "2", "1", "8", "1", "2", "1", "12", "1", "2", "3", "1", "1", "2", "1", "2", "1", "2", "1", "12", "1", "2", "3", "2", "1", "2", "1", "10", "1", "2", "1", "12", "1", "2", "1", "8", "1", "6", "1", "2", "1", "2", "1", "12", "1", "2", "3", "1", "1", "2", "1", "8", "1" ]
[ "nonn" ]
40
1
2
[ "A000005", "A009191", "A009194", "A009195", "A009205", "A009213", "A009230", "A046642", "A049820", "A125168", "A138010", "A286540", "A303781", "A318459", "A319337", "A322979", "A322980", "A323073", "A324553" ]
null
David W. Wilson
2019-03-31T04:09:15
oeisdata/seq/A009/A009191.seq
53c826023317c213598da4330a1fa811
A009192
E.g.f. exp(log(1+x)*cos(x)).
[ "1", "1", "0", "-3", "-6", "15", "75", "84", "-1820", "-123", "-10725", "475816", "-3554562", "32763107", "-501958275", "6877337128", "-95130710792", "1486984480729", "-24736452203529", "430314112493264", "-7930867848273070", "154362838472661367", "-3154456665148212743" ]
[ "sign", "easy" ]
17
0
4
null
null
R. H. Hardin
2018-07-28T16:23:45
oeisdata/seq/A009/A009192.seq
d504180c2bf010d773201673e24d2462
A009193
Expansion of e.g.f.: exp(log(1+x)*cosh(x)).
[ "1", "1", "0", "3", "6", "-5", "135", "-154", "1260", "6189", "-33285", "470294", "-2056758", "14299935", "-3614611", "-379101878", "10041282472", "-121491285111", "1656259499511", "-21619048472474", "338632378045750", "-5874571029856693", "115201962050532137" ]
[ "sign", "easy" ]
15
0
4
null
null
R. H. Hardin
2018-07-28T16:43:13
oeisdata/seq/A009/A009193.seq
fbd8915b6a4e0264b70806473cccf805
A009194
a(n) = gcd(n, sigma(n)).
[ "1", "1", "1", "1", "1", "6", "1", "1", "1", "2", "1", "4", "1", "2", "3", "1", "1", "3", "1", "2", "1", "2", "1", "12", "1", "2", "1", "28", "1", "6", "1", "1", "3", "2", "1", "1", "1", "2", "1", "10", "1", "6", "1", "4", "3", "2", "1", "4", "1", "1", "3", "2", "1", "6", "1", "8", "1", "2", "1", "12", "1", "2", "1", "1", "1", "6", "1", "2", "3", "2", "1", "3", "1", "2", "1", "4", "1", "6", "1", "2", "1", "2", "1", "28", "1", "2", "3", "4", "1", "18", "7", "4", "1", "2", "5", "12", "1", "1", "3", "1", "1", "6", "1", "2" ]
[ "nonn" ]
49
1
6
[ "A000203", "A003624", "A007691", "A009191", "A009194", "A009205", "A009242", "A014567", "A017666", "A063906", "A069059", "A073802", "A082062", "A179931", "A205523", "A216793", "A234367", "A249917", "A274382", "A286591", "A286594" ]
null
David W. Wilson
2024-02-07T01:16:00
oeisdata/seq/A009/A009194.seq
59df3c266b5286ffcce75e60435d9c3f
A009195
a(n) = gcd(n, phi(n)).
[ "1", "1", "1", "2", "1", "2", "1", "4", "3", "2", "1", "4", "1", "2", "1", "8", "1", "6", "1", "4", "3", "2", "1", "8", "5", "2", "9", "4", "1", "2", "1", "16", "1", "2", "1", "12", "1", "2", "3", "8", "1", "6", "1", "4", "3", "2", "1", "16", "7", "10", "1", "4", "1", "18", "5", "8", "3", "2", "1", "4", "1", "2", "9", "32", "1", "2", "1", "4", "1", "2", "1", "24", "1", "2", "5", "4", "1", "6", "1", "16", "27", "2", "1", "12", "1", "2", "1", "8", "1", "6", "1", "4", "3", "2", "1", "32", "1", "14", "3", "20" ]
[ "nonn", "easy", "nice" ]
51
1
4
[ "A000010", "A003277", "A009195", "A050399", "A051953", "A061303", "A109395", "A285711" ]
null
David W. Wilson
2024-02-22T09:09:14
oeisdata/seq/A009/A009195.seq
98ebfc4e1652032b080debf127b86461
A009196
Expansion of e.g.f. exp(log(1+x)/cos(x)).
[ "1", "1", "0", "3", "6", "15", "195", "126", "6860", "10581", "275955", "1581734", "11684442", "223836379", "423165561", "32439219242", "10301267912", "4976257880345", "4959730228167", "803695677341350", "3521551886934550", "131556027669677615", "1743242423131143869", "19663074849601180770" ]
[ "sign", "easy" ]
19
0
4
null
null
R. H. Hardin
2018-02-25T20:39:28
oeisdata/seq/A009/A009196.seq
a26e46b844acddbf6fadc90ffc9c92fb
A009197
Expansion of exp(log(1+x)/cosh(x)).
[ "1", "1", "0", "-3", "-6", "35", "135", "-476", "-6300", "14349", "298515", "254056", "-26673042", "-26975169", "1931306377", "16803854768", "-336040323112", "-1435742838615", "20743481564487", "843925791375728", "-11354618863953550", "-37784454009996005" ]
[ "sign", "easy" ]
13
0
4
null
null
R. H. Hardin
2015-07-02T12:46:32
oeisdata/seq/A009/A009197.seq
9cb2c8b85e6187760720e3fc5d09990c
A009198
E.g.f. exp(log(1+x)/exp(x)).
[ "1", "1", "-2", "0", "18", "-85", "155", "1057", "-13636", "86361", "-271783", "-1518539", "35743378", "-376883351", "2663534939", "-8383983593", "-117620643336", "2907896789457", "-39364767602331", "389671721253889", "-2504052803057234", "-3842812946739679", "465976686530941599" ]
[ "sign", "easy" ]
20
0
3
null
null
R. H. Hardin
2022-05-13T12:45:05
oeisdata/seq/A009/A009198.seq
d92dd5668ba75b08718505b528a00690
A009199
Expansion of e.g.f. exp(log(1+x)^2).
[ "1", "0", "2", "-6", "34", "-220", "1688", "-14868", "147684", "-1631376", "19821912", "-262573080", "3764276712", "-58044604176", "957653604672", "-16828739439120", "313742795670288", "-6183918938706048", "128463999017594016", "-2804979941504113248" ]
[ "sign", "easy" ]
29
0
3
null
null
R. H. Hardin
2022-05-06T13:31:41
oeisdata/seq/A009/A009199.seq
6104530641cb7b7a1395d6362cefd2cb
A009200
E.g.f. exp(sin(log(1+x))).
[ "1", "1", "0", "-1", "2", "-4", "16", "-120", "1084", "-10568", "111196", "-1269764", "15728360", "-210510936", "3029497472", "-46654106824", "765497451536", "-13330741903360", "245546485746064", "-4769321293582128", "97417091239222336", "-2087367002843576384", "46814167766826521920", "-1096698328458955351616" ]
[ "sign", "easy" ]
20
0
5
[ "A002017", "A009200" ]
null
R. H. Hardin
2017-04-01T12:31:10
oeisdata/seq/A009/A009200.seq
8bc2b267c1f25277b618fefa449e9441