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oeis

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348
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int64
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2.31k
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int64
-14,827
666,262,453B
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timestamp
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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A009001
Expansion of e.g.f: (1+x)*cos(x).
[ "1", "1", "-1", "-3", "1", "5", "-1", "-7", "1", "9", "-1", "-11", "1", "13", "-1", "-15", "1", "17", "-1", "-19", "1", "21", "-1", "-23", "1", "25", "-1", "-27", "1", "29", "-1", "-31", "1", "33", "-1", "-35", "1", "37", "-1", "-39", "1", "41", "-1", "-43", "1", "45", "-1", "-47", "1", "49", "-1", "-51", "1", "53", "-1", "-55", "1", "57", "-1", "-59", "1", "61", "-1", "-63", "1", "65", "-1", "-67", "1", "69", "-1", "-71", "1", "73", "-1", "-75", "1", "77", "-1", "-79", "1", "81", "-1", "-83", "1", "85" ]
[ "sign", "easy", "nice" ]
70
0
4
[ "A009001", "A009531", "A049471" ]
null
R. H. Hardin, N. J. A. Sloane, Simon Plouffe, David W. Wilson
2024-12-23T17:48:16
oeisdata/seq/A009/A009001.seq
9270aebd25cd13452364f2f7ee411081
A009002
Expansion of (1+x)/cos(x).
[ "1", "1", "1", "3", "5", "25", "61", "427", "1385", "12465", "50521", "555731", "2702765", "35135945", "199360981", "2990414715", "19391512145", "329655706465", "2404879675441", "45692713833379", "370371188237525", "7777794952988025", "69348874393137901", "1595024111042171723", "15514534163557086905" ]
[ "nonn" ]
32
0
4
null
null
R. H. Hardin
2024-12-29T21:41:59
oeisdata/seq/A009/A009002.seq
e394fc40f904e34b56cc7835ca0a720c
A009003
Hypotenuse numbers (squares are sums of 2 nonzero squares).
[ "5", "10", "13", "15", "17", "20", "25", "26", "29", "30", "34", "35", "37", "39", "40", "41", "45", "50", "51", "52", "53", "55", "58", "60", "61", "65", "68", "70", "73", "74", "75", "78", "80", "82", "85", "87", "89", "90", "91", "95", "97", "100", "101", "102", "104", "105", "106", "109", "110", "111", "113", "115", "116", "117", "119", "120", "122", "123", "125", "130", "135", "136", "137", "140" ]
[ "nonn" ]
143
1
1
[ "A002144", "A004144", "A004431", "A004613", "A006339", "A009000", "A009003", "A024507", "A072592", "A083025", "A084645", "A084646", "A084647", "A084648", "A084649", "A146984", "A187811" ]
null
David W. Wilson
2024-07-06T14:01:35
oeisdata/seq/A009/A009003.seq
b3a4787869fe68fd4d569146040b3999
A009004
Ordered short legs of Pythagorean triangles.
[ "3", "5", "6", "7", "8", "9", "9", "10", "11", "12", "12", "13", "14", "15", "15", "15", "16", "16", "17", "18", "18", "19", "20", "20", "20", "21", "21", "21", "22", "23", "24", "24", "24", "24", "25", "25", "26", "27", "27", "27", "28", "28", "28", "29", "30", "30", "30", "31", "32", "32", "32", "33", "33", "33", "33", "34", "35", "35", "35", "36", "36", "36", "36", "36", "37", "38", "39", "39", "39", "39", "40", "40", "40", "40" ]
[ "nonn" ]
15
1
1
null
null
David W. Wilson
2013-07-26T10:17:25
oeisdata/seq/A009/A009004.seq
621f3d2f7f7ab967e57ac780ffe3c1de
A009005
All natural numbers except 1, 2 and 4.
[ "3", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74", "75", "76", "77" ]
[ "nonn", "easy" ]
33
1
1
[ "A000203", "A000217", "A009005", "A242963" ]
null
David W. Wilson
2024-12-02T16:29:05
oeisdata/seq/A009/A009005.seq
42e3c95a9b0af2b5a173f1ea734707d3
A009006
Expansion of e.g.f.: 1 + tan(x).
[ "1", "1", "0", "2", "0", "16", "0", "272", "0", "7936", "0", "353792", "0", "22368256", "0", "1903757312", "0", "209865342976", "0", "29088885112832", "0", "4951498053124096", "0", "1015423886506852352", "0", "246921480190207983616", "0", "70251601603943959887872", "0", "23119184187809597841473536", "0" ]
[ "nonn", "easy" ]
102
0
4
[ "A000182", "A009006" ]
null
R. H. Hardin
2024-12-29T21:41:42
oeisdata/seq/A009/A009006.seq
11b159c5cb4572767e313285953789c1
A009007
Expansion of 1/cos(log(1+x)).
[ "1", "0", "1", "-3", "16", "-100", "760", "-6720", "67940", "-772560", "9760100", "-135617900", "2055532400", "-33748556400", "596675513200", "-11302050942000", "228340292986000", "-4901379615184000", "111394219174810000", "-2672242230261006000" ]
[ "sign" ]
21
0
4
null
null
R. H. Hardin, Simon Plouffe
2022-09-08T08:44:37
oeisdata/seq/A009/A009007.seq
aa289206832663034ab6ca7f552bc686
A009008
Expansion of e.g.f.: 1/cos(sin(x)) (even-indexed coefficients only).
[ "1", "1", "1", "-23", "-415", "849", "421089", "16027897", "-602344127", "-137830187103", "-6375572516543", "1282077224074761", "294398207479497377", "6767832711454751473", "-10535904130516747834591", "-2468712006908963695579879", "172926818125145929773139073" ]
[ "sign" ]
25
0
4
null
null
R. H. Hardin, Simon Plouffe
2023-10-27T21:10:53
oeisdata/seq/A009/A009008.seq
c977d68594d2f27488db8bee2e895c73
A009009
Expansion of e.g.f.: 1/cos(sinh(x)) (even-indexed coefficients only).
[ "1", "1", "9", "177", "6545", "387649", "33646041", "4025701617", "635120351777", "127753094128897", "31911422805749673", "9691219439564235441", "3516474983468155702193", "1502487398886128051614273", "746659439867912626958616441", "427003792367575880943003380721" ]
[ "nonn" ]
35
0
3
null
null
R. H. Hardin
2018-07-21T20:26:56
oeisdata/seq/A009/A009009.seq
8aba321d2724aa873741138746c1d185
A009010
Expansion of e.g.f.: 1/cos(tan(x)) (even-indexed coefficients only).
[ "1", "1", "13", "397", "22265", "1996569", "262056837", "47378857957", "11289999097969", "3429209143916337", "1293273763150662781", "592937704157794933821", "324791587492604492427881", "209490216975221386279672393", "157153880464155360205476452597" ]
[ "nonn" ]
29
0
3
null
null
R. H. Hardin
2018-07-21T20:26:28
oeisdata/seq/A009/A009010.seq
6ed20fdef984ee1dd0d463da628e04af
A009011
Expansion of e.g.f.: 1/cos(tanh(x)) (even-indexed coefficients only).
[ "1", "1", "-3", "-3", "665", "-25031", "607893", "13065717", "-3684215119", "322746228337", "-2173907680851", "-5317484317809939", "1007358319257596489", "46704901267812186793", "-111828938184578058229947", "54497429277597236190513381", "-19349766542166780916394521759" ]
[ "sign" ]
24
0
3
null
null
R. H. Hardin
2018-07-21T20:54:52
oeisdata/seq/A009/A009011.seq
338d2f9c43fb5e398846815b1de13d51
A009012
Ordered long legs of Pythagorean triangles.
[ "4", "8", "12", "12", "15", "16", "20", "21", "24", "24", "24", "28", "30", "32", "35", "36", "36", "40", "40", "42", "44", "45", "45", "48", "48", "48", "52", "55", "56", "56", "60", "60", "60", "60", "63", "63", "64", "68", "70", "72", "72", "72", "72", "75", "76", "77", "80", "80", "80", "84", "84", "84", "84", "88", "90", "90", "91", "92", "96", "96", "96", "99", "100", "104", "105", "105", "105", "105", "108" ]
[ "nonn" ]
6
1
1
[ "A009012", "A046084" ]
null
David W. Wilson
2012-03-30T18:35:07
oeisdata/seq/A009/A009012.seq
ef00bbf37898b94ab2992ecc97e620d6
A009013
Expansion of E.g.f.: 1/(cosh(x)*cos(x)) (only powers that are multiples of 4).
[ "1", "4", "1104", "2154304", "15456463104", "295213107733504", "12366226074019221504", "998143138923599406383104", "141496025961835234723147874304", "32857017298796399667445911477551104", "11837460622615877064781409516336792469504" ]
[ "nonn" ]
29
0
2
null
null
R. H. Hardin
2018-07-21T23:38:11
oeisdata/seq/A009/A009013.seq
26527dc324654078251981e76b1ff28b
A009014
Expansion of E.g.f.: (1 + x)/(1 + x + x^2/2).
[ "1", "0", "-1", "3", "-6", "0", "90", "-630", "2520", "0", "-113400", "1247400", "-7484400", "0", "681080400", "-10216206000", "81729648000", "0", "-12504636144000", "237588086736000", "-2375880867360000", "0", "548828480360160000", "-12623055048283680000" ]
[ "sign", "easy" ]
25
0
4
[ "A009014", "A009116", "A009769" ]
null
R. H. Hardin
2018-07-21T23:38:16
oeisdata/seq/A009/A009014.seq
403e86dd90623fea52f3c7934b5b8e91
A009015
Expansion of e.g.f.: cos(x*cos(x)) (even powers only).
[ "1", "-1", "13", "-181", "3865", "-140521", "6324517", "-344747677", "23853473329", "-1996865965009", "193406280000061", "-21615227339380357", "2778071540350106953", "-403985610499148666041", "65635628800688339178325", "-11851572489741709802698861", "2366329597668159364674862177" ]
[ "sign", "changed" ]
24
0
3
null
null
R. H. Hardin
2025-04-16T09:01:37
oeisdata/seq/A009/A009015.seq
76d62dc565f04ce56412151d078aacd9
A009016
Expansion of E.g.f.: cos(cosh(x)*x) (even powers only).
[ "1", "-1", "-11", "-61", "1737", "88679", "2086525", "-45950997", "-9763133167", "-705668046769", "-17356978593659", "3823112141007763", "788728947108214489", "82036502117747569079", "1412038521698998808077" ]
[ "sign" ]
13
0
3
null
null
R. H. Hardin
2018-07-21T23:38:32
oeisdata/seq/A009/A009016.seq
6aa39171bb50d865a9f560ab4562234f
A009017
Expansion of e.g.f. cos(x*exp(x)).
[ "1", "0", "-1", "-6", "-23", "-60", "-1", "1526", "15121", "106344", "579359", "1870418", "-8716487", "-251210388", "-3217413473", "-31518844530", "-245728084447", "-1260370850736", "3075924210623", "208464730479658", "3846319817704841", "52691292058337940" ]
[ "sign", "easy" ]
20
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009017.seq
f3693bf559205b2a151a1b9a672b8109
A009018
Expansion of e.g.f.: cos(log(1+log(1+x))).
[ "1", "0", "-1", "6", "-39", "295", "-2589", "26026", "-295754", "3755016", "-52729546", "811837268", "-13601028438", "246312375686", "-4793646410058", "99730695561532", "-2207506199891660", "51757576802639920", "-1280121375188444260" ]
[ "sign", "easy" ]
21
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009018.seq
529d1a7bd0f35d15b2b9bcba5c121917
A009019
Expansion of cos(log(1 + sin(x))).
[ "1", "0", "-1", "3", "-6", "10", "-6", "-77", "724", "-5220", "36364", "-259457", "1933704", "-15161250", "125278984", "-1090268137", "9973751184", "-95650827080", "958577301104", "-10001308630117", "108164953941664", "-1206196891901710", "13774788612312224" ]
[ "sign", "easy" ]
15
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009019.seq
6c1ff044854b07abfbba6e666845b5df
A009020
Expansion of e.g.f.: cos(log(1 + sinh(x))).
[ "1", "0", "-1", "3", "-14", "70", "-406", "2723", "-20684", "176100", "-1661236", "17182143", "-193042904", "2335585330", "-30176889016", "412862112263", "-5925850093424", "88231921922760", "-1341868300356496", "20329433614333083", "-291715707804107744" ]
[ "sign", "easy" ]
20
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009020.seq
3df19732052fead17c34bec32da28c37
A009021
Expansion of e.g.f. cos(log(1+tan(x))).
[ "1", "0", "-1", "3", "-18", "100", "-726", "5698", "-52028", "522720", "-5849876", "71473468", "-951628488", "13674233040", "-211091632376", "3478906531688", "-60920066577648", "1127785660994560", "-21969631512312976", "448167387287730608" ]
[ "sign", "easy" ]
28
0
4
null
null
R. H. Hardin
2025-04-10T21:17:47
oeisdata/seq/A009/A009021.seq
8cca7e3ac99479d360ef70abde114128
A009022
Expansion of e.g.f. cos(log(1+tanh(x))).
[ "1", "0", "-1", "3", "-2", "-20", "74", "98", "-1532", "960", "41324", "-105732", "-1595912", "7998640", "85401224", "-705417112", "-6026865392", "76352075520", "537223559024", "-10130428275792", "-58185728893472", "1628892022801600", "7352490891960224", "-313251680404802272", "-1026222973696521152" ]
[ "sign", "easy", "changed" ]
36
0
4
null
null
R. H. Hardin
2025-04-16T09:01:43
oeisdata/seq/A009/A009022.seq
ab5f78971d64d556dcbf2c7a9c1f5f38
A009023
Long legs of Pythagorean triangles.
[ "4", "8", "12", "15", "16", "20", "21", "24", "28", "30", "32", "35", "36", "40", "42", "44", "45", "48", "52", "55", "56", "60", "63", "64", "68", "70", "72", "75", "76", "77", "80", "84", "88", "90", "91", "92", "96", "99", "100", "104", "105", "108", "110", "112", "116", "117", "120", "124", "126", "128", "132", "135", "136", "140", "143", "144", "147", "148", "150", "152", "153", "154", "156" ]
[ "nonn" ]
34
1
1
[ "A009012", "A009023", "A046084", "A074235", "A227481" ]
null
David W. Wilson
2019-01-19T03:17:26
oeisdata/seq/A009/A009023.seq
6ac7aa1aa7026dcf95323f337595f48f
A009024
Expansion of e.g.f.: x*cos(log(1+x)).
[ "0", "1", "0", "-3", "12", "-50", "240", "-1330", "8400", "-59580", "468000", "-4018300", "37237200", "-367507400", "3802780800", "-40373385000", "423927504000", "-4048235126000", "25093796832000", "288695417426000", "-18721925937000000", "623644389813900000" ]
[ "sign", "easy" ]
22
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009024.seq
4599053d28328e9da9bc2e5a036dc07a
A009025
Expansion of e.g.f.: cos(log(1+x))/cos(x).
[ "1", "0", "0", "3", "-11", "70", "-354", "2415", "-15763", "125172", "-1002604", "9222455", "-86960631", "905535618", "-9647654054", "109599211995", "-1245410413895", "14255558592040", "-147402624694104", "1100681059753035", "7361694753788285", "-667740119513804610" ]
[ "sign", "easy" ]
22
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009025.seq
97bd9a9ab08380e2c0ffc78528e9c436
A009026
Expansion of cos(log(1+x))/cosh(x).
[ "1", "0", "-2", "3", "1", "10", "-176", "735", "-1707", "18828", "-251646", "1819895", "-10653939", "114938382", "-1464499076", "11843786955", "-40962861815", "-513203638440", "26152049892934", "-897502828846005", "24985080257574265", "-628449474239226990" ]
[ "sign", "easy" ]
17
0
3
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009026.seq
2887e003867635f9a417f68a187bf26b
A009027
Expansion of cos(log(1+x))/exp(x).
[ "1", "-1", "0", "5", "-27", "129", "-654", "3695", "-23475", "166727", "-1309684", "11244309", "-104234215", "1029821545", "-10679924202", "113869873039", "-1205722312839", "11744215117935", "-79159333236840", "-612589942020923", "48022885459499181", "-1644758184992095631" ]
[ "sign", "easy" ]
15
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009027.seq
f818a67520d0af8343d9e2f2863b2c73
A009028
Expansion of cos(log(1+x)*cos(x)).
[ "1", "0", "-1", "3", "2", "-20", "-40", "630", "-3092", "13032", "-133580", "1827980", "-21237632", "244445760", "-3154775208", "45173375520", "-689191245168", "11093076554048", "-189142200382672", "3415285850672880", "-65041019882791840", "1301902345882783680" ]
[ "sign", "easy" ]
21
0
4
null
null
R. H. Hardin
2024-12-29T21:41:29
oeisdata/seq/A009/A009028.seq
5b90753875263d2109a452c98214dcae
A009029
Expansion of cos(log(1+x)*cosh(x)).
[ "1", "0", "-1", "3", "-22", "100", "-580", "3150", "-16868", "80568", "-141500", "-4254580", "105666112", "-1880236800", "31074394312", "-508890083520", "8476622031888", "-145412857677888", "2584745973422384", "-47756915743199760", "918437313488897760" ]
[ "sign", "easy" ]
17
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009029.seq
e9865871fd0167521b0cccd906d3684e
A009030
Expansion of e.g.f. cos(log(1+x)*exp(x)).
[ "1", "0", "-1", "-3", "-10", "-10", "-10", "560", "1220", "24936", "-53660", "1220252", "-13415576", "140346648", "-2192051992", "28246127520", "-453007180912", "7224412576832", "-124772679402064", "2275818139520912", "-43588354415158432", "881182228173945952" ]
[ "sign", "easy" ]
22
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009030.seq
56efc9fad00d41bb70e707019c287046
A009031
Expansion of cos(x*log(1+x)).
[ "1", "0", "0", "0", "-12", "60", "-330", "2100", "-13664", "96768", "-747720", "6233040", "-55757592", "529420320", "-5249506080", "53003714400", "-519287424000", "4336798757760", "-12704182464960", "-768063270038400", "31846322269825920", "-952431265450344960" ]
[ "sign", "easy" ]
15
0
5
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009031.seq
c4c39f3f38bfc18cc5d0c2f3b688eea7
A009032
Expansion of cos(log(1+x)/cos(x)).
[ "1", "0", "-1", "3", "-22", "100", "-700", "3990", "-28628", "171288", "-1025420", "1661660", "78215392", "-2266954560", "46180065256", "-873515610240", "16163533621648", "-300558671466048", "5688054655288496", "-109993409199908496", "2184633395323803360" ]
[ "sign", "easy" ]
16
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009032.seq
8c3607b4aaf47cc46a1c3687afe21090
A009033
Expansion of e.g.f.: cos(log(1+x)/cosh(x)).
[ "1", "0", "-1", "3", "2", "-20", "-160", "1470", "-1412", "-17208", "-311900", "5526620", "-27336032", "64471680", "-3978938184", "91242933600", "-974175281648", "9223539606848", "-209919913406800", "4978659648353904", "-83195760215366560", "1324088843470088640" ]
[ "sign", "easy" ]
20
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009033.seq
3791dcbd8b921dd23d3c7c0415844fb0
A009034
Expansion of e.g.f. cos(log(1+x)/exp(x)).
[ "1", "0", "-1", "9", "-58", "330", "-1690", "6580", "5924", "-626856", "11483620", "-169739812", "2336104168", "-31232156280", "411116838184", "-5322020904720", "66716820030608", "-776290733888320", "7344102656963504", "-19147581666874928" ]
[ "sign", "easy" ]
22
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009034.seq
bec16a9bc1cb6c33a06beb59d65361be
A009035
Expansion of e.g.f.: cos(log(1+x)^2).
[ "1", "0", "0", "0", "-12", "120", "-1020", "8820", "-79548", "746928", "-7222560", "70422000", "-663291552", "5383325376", "-19385922192", "-677619961200", "27837247597392", "-777514428757632", "19561790897109504", "-475628128967428992", "11488209552378045888" ]
[ "sign", "easy" ]
19
0
5
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009035.seq
9ece6de15144dc48923fc2b3b5ef78df
A009036
Expansion of cos(sin(log(1+x))).
[ "1", "0", "-1", "3", "-6", "0", "114", "-1134", "9320", "-75456", "640144", "-5888080", "59989416", "-683640048", "8694795576", "-122022500040", "1861267622656", "-30418406611456", "526523001326720", "-9570437327493504", "181530307816180736", "-3575813555711685120" ]
[ "sign", "easy" ]
14
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009036.seq
642a0667dfe06fcb451fd09bdbeba1f1
A009037
Expansion of E.g.f. cos(sin(sin(x))), even powers only.
[ "1", "-1", "9", "-153", "4273", "-177489", "10342137", "-800697641", "78896218081", "-9587206592289", "1403875965476969", "-243412313149166137", "49273184499900888465", "-11506634193913551650161", "3067851166645384439929945" ]
[ "sign" ]
14
0
3
null
null
R. H. Hardin
2018-07-22T22:53:29
oeisdata/seq/A009/A009037.seq
75db238bbfa03aa3b062e2371de16111
A009038
Expansion of E.g.f. cos(sin(sinh(x))), even powers only.
[ "1", "-1", "1", "47", "1", "-13409", "77441", "19836879", "-535288319", "-139742075329", "-2263631905535", "1157041164813423", "85544399896958465", "-10251042205544240161", "-896378013566768664703", "524122354739233459190287" ]
[ "sign" ]
16
0
4
null
null
R. H. Hardin
2018-07-22T22:53:33
oeisdata/seq/A009/A009038.seq
5ccedee235ceb10d13d1b2ea40866c3c
A009039
Expansion of E.g.f. cos(sin(tan(x))), even powers only.
[ "1", "-1", "-3", "27", "2425", "143031", "8956533", "618394579", "46232494321", "3608163168111", "254307747662573", "-15725973912655477", "-32163339922362247575", "-26444005741558393208281", "-19705272022676306432282267" ]
[ "sign" ]
14
0
3
null
null
R. H. Hardin
2018-07-22T22:53:39
oeisdata/seq/A009/A009039.seq
28a164f00b140e93136d3a76134b393f
A009040
Expansion of E.g.f. cos(sin(tanh(x))), even powers only.
[ "1", "-1", "13", "-373", "18649", "-1433129", "156563045", "-23043285021", "4392102360241", "-1051530622359889", "308633929353801661", "-108880766753141666757", "45418989883077539513225", "-22097331609699052757909881" ]
[ "sign" ]
20
0
3
null
null
R. H. Hardin
2018-07-22T22:53:47
oeisdata/seq/A009/A009040.seq
7fb03455cd922ce0142e851e9b7c2451
A009041
Ordered legs of Pythagorean triangles.
[ "3", "4", "5", "6", "7", "8", "8", "9", "9", "10", "11", "12", "12", "12", "12", "13", "14", "15", "15", "15", "15", "16", "16", "16", "17", "18", "18", "19", "20", "20", "20", "20", "21", "21", "21", "21", "22", "23", "24", "24", "24", "24", "24", "24", "24", "25", "25", "26", "27", "27", "27", "28", "28", "28", "28", "29", "30", "30", "30", "30", "31", "32", "32", "32", "32", "33", "33", "33", "33", "34", "35", "35", "35", "35", "36" ]
[ "nonn" ]
20
1
1
[ "A009004", "A009012", "A009041" ]
null
David W. Wilson
2018-04-19T10:06:31
oeisdata/seq/A009/A009041.seq
2a7fdf272bcbbd77ceae83fd8dee1dd0
A009042
Expansion of x*cos(sin(x)), odd terms only.
[ "1", "-3", "25", "-259", "4113", "-89859", "2452905", "-82466115", "3364642465", "-162289204995", "9080010901689", "-582825476943747", "42497355011746225", "-3485070555315399171", "318706043315086782281", "-32281156967340604488131" ]
[ "sign" ]
14
0
2
null
null
R. H. Hardin
2018-07-24T02:58:08
oeisdata/seq/A009/A009042.seq
dd8411566c18990b0fdf719266c1652c
A009043
Expansion of cos(sin(x))/cos(x), even terms only.
[ "1", "0", "4", "24", "848", "25792", "1491392", "106879616", "10504954112", "1298259085312", "200164547589120", "37466482286032896", "8382720548500262912", "2208241619066995294208", "676599830605856131694592" ]
[ "nonn" ]
14
0
3
null
null
R. H. Hardin
2018-07-24T02:58:17
oeisdata/seq/A009/A009043.seq
b503c197d896bd1f9c86c09b25b9a60f
A009044
Expansion of cos(sin(x))/cosh(x), even terms only.
[ "1", "-2", "16", "-248", "6336", "-244480", "13409408", "-999327488", "97590304768", "-12120423043072", "1867576863899648", "-349745166753398784", "78248003933970006016", "-20613585750577859067904", "6315933020629432945606656" ]
[ "sign" ]
17
0
2
null
null
R. H. Hardin
2018-07-24T02:58:22
oeisdata/seq/A009/A009044.seq
d3b2fade3f1560459f265fd7ca36d3fc
A009045
Expansion of cos(sin(x))/exp(x).
[ "1", "-1", "0", "2", "0", "-16", "24", "104", "-256", "-1600", "5632", "29952", "-156032", "-644736", "4761600", "18383616", "-178225152", "-645554176", "8081772544", "25645936640", "-422364381184", "-1160636121088", "25184814366720", "60217271582720", "-1713906141986816" ]
[ "sign", "easy" ]
19
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009045.seq
fe65e2a631248dc1e4d5a3b31f7aaa3c
A009046
Expansion of cos(sin(x)*cos(x)), even terms only.
[ "1", "-1", "17", "-337", "9697", "-451809", "29324913", "-2348275633", "229227939521", "-27378158737089", "3912000089144273", "-649905519911431953", "123605642085065411233", "-26737890902906532576673", "6532350281317524911044657", "-1785601511004402102425350001" ]
[ "sign" ]
15
0
3
null
null
R. H. Hardin
2018-07-24T02:58:33
oeisdata/seq/A009/A009046.seq
1992d1a4f0dceda0bfc79fcddba9b551
A009047
Expansion of cos(sin(x)*cosh(x)), even terms only.
[ "1", "-1", "-7", "23", "1297", "-6129", "-894903", "829671", "1879275169", "1886150559", "-7580265762535", "-85001467923145", "61409100961369265", "1056714909891968687", "-781355567634874555799", "-25440890573992236442361" ]
[ "sign" ]
18
0
3
null
null
R. H. Hardin
2018-07-24T02:58:42
oeisdata/seq/A009/A009047.seq
808e791af3813fc4515dfa3d387e6323
A009048
Expansion of e.g.f. cos(sin(x)*exp(x)).
[ "1", "0", "-1", "-6", "-19", "-20", "203", "1862", "9305", "20472", "-159849", "-2441230", "-17558715", "-60043100", "365766243", "8445023358", "80287239857", "383311153776", "-1756145007825", "-61596647223446", "-735340088843107", "-4522824431862308", "15016682566162427", "819555396311083830" ]
[ "sign", "easy", "changed" ]
33
0
4
null
null
R. H. Hardin
2025-04-16T08:37:59
oeisdata/seq/A009/A009048.seq
d6481daf6b35a9b46b48c994ad7c30d9
A009049
Expansion of cos(sin(x)*log(1+x)).
[ "1", "0", "0", "0", "-12", "60", "-210", "1260", "-8400", "54432", "-456360", "4469520", "-45154296", "493288224", "-5892938688", "75085701600", "-1017515316480", "14668694264704", "-223340767219392", "3570533188036992", "-59698808359690112", "1038791996385239040" ]
[ "sign", "easy" ]
14
0
5
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009049.seq
65c1735f092df69138a6b28e405d9a78
A009050
Expansion of e.g.f. cos(x*sin(x)) (even power only).
[ "1", "0", "-12", "120", "784", "-95040", "3292608", "-9423232", "-9230042880", "890079012864", "-40083887897600", "-2468650419873792", "837675174905843712", "-109581967679961088000", "5834566862721760149504" ]
[ "sign" ]
21
0
3
null
null
R. H. Hardin
2018-07-24T09:41:13
oeisdata/seq/A009/A009050.seq
d9f9433efd050055a8d4e14c618e27ec
A009051
Expansion of e.g.f. cos(sin(x)/cosh(x)), even powers only.
[ "1", "-1", "17", "-457", "19777", "-1305489", "122670033", "-15462740633", "2502900454401", "-504155298072609", "123438576028985873", "-36064963500185608553", "12385279694301347665473", "-4936243039568368083279793", "2258619438301840395444067537", "-1175352020113183347337766918201" ]
[ "sign" ]
21
0
3
null
null
R. H. Hardin
2018-07-24T11:49:42
oeisdata/seq/A009/A009051.seq
eb0eec94f5091b4d03fb2e68f9bd53b3
A009052
Expansion of e.g.f. cos(sin(x)^2), even terms only.
[ "1", "0", "-12", "240", "-2352", "-136320", "15140928", "-971093760", "28387408128", "4688909905920", "-1262963768650752", "191995869733662720", "-17544464368915034112", "-1212607904700871311360", "1171249187182930708021248" ]
[ "sign" ]
17
0
3
null
null
R. H. Hardin
2018-07-24T11:49:52
oeisdata/seq/A009/A009052.seq
33ac3f99cac11191cd96016f8b88a2bf
A009053
Expansion of e.g.f. cos(sinh(log(1+x))).
[ "1", "0", "-1", "3", "-14", "80", "-526", "3906", "-32192", "290016", "-2816056", "29050120", "-313052024", "3442154352", "-37060529416", "353733158520", "-1866295941824", "-42066299646976", "2247562825065152", "-73960387213018176", "2159580310527713536" ]
[ "sign", "easy" ]
20
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009053.seq
cf3e01ca4fa3a1ada881345f819d018c
A009054
Expansion of e.g.f. cos(sinh(sin(x))), even terms only.
[ "1", "-1", "1", "47", "-895", "31", "1002497", "-53580465", "-8587007", "305732208959", "-30437638147583", "-144862063593105", "545283874522872193", "-85823970766230251681", "-801780964397998270975", "3637965188578615382687887" ]
[ "sign" ]
21
0
4
null
null
R. H. Hardin
2018-07-24T03:11:12
oeisdata/seq/A009/A009054.seq
7358aa9b01d68ae7ac26da894749d74b
A009055
Expansion of e.g.f. cos(sinh(tan(x))), even terms only.
[ "1", "-1", "-11", "-253", "-9463", "-491609", "-30257347", "-1480493589", "177416283793", "125705754161615", "53738108098148101", "22477151211215445843", "9977406312993326490265", "4802660699035958910256759" ]
[ "sign" ]
18
0
3
null
null
R. H. Hardin
2018-07-24T03:11:44
oeisdata/seq/A009/A009055.seq
abd2f2ea3d93826ef514a57ebc171598
A009056
Numbers >= 3.
[ "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "64", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74", "75", "76", "77" ]
[ "easy", "nonn" ]
24
1
1
[ "A009005", "A009056", "A020739", "A055998" ]
null
David W. Wilson
2024-11-01T09:35:34
oeisdata/seq/A009/A009056.seq
e912aa122c1fec5d23156f92876b0a42
A009057
Expansion of e.g.f. x*cos(sinh(x)) (odd powers only).
[ "1", "-3", "-15", "21", "1953", "32461", "77649", "-18557595", "-894805183", "-21405607651", "421226202033", "90171090228021", "6418365899545825", "230309031988304109", "-11126456208720437487", "-3093396343171182148731", "-342554566975833968005503" ]
[ "sign" ]
22
0
2
null
null
R. H. Hardin
2018-07-24T03:11:56
oeisdata/seq/A009/A009057.seq
aa34da461e47e3111108afd519eb56f2
A009058
Expansion of e.g.f. cos(sinh(x))/cos(x), even terms only.
[ "1", "0", "-4", "-56", "-1072", "-34368", "-1781440", "-132000896", "-12912385792", "-1604411553792", "-247155791205376", "-46275148760619008", "-10352111715031035904", "-2727077778568910979072", "-835562477291891829882880" ]
[ "sign" ]
18
0
3
null
null
R. H. Hardin
2018-07-24T09:41:21
oeisdata/seq/A009/A009058.seq
6e0d6da42393cbc260965e2771f5d05e
A009059
Expansion of e.g.f. cos(sinh(x))/exp(x).
[ "1", "-1", "0", "2", "-8", "24", "-56", "104", "64", "-1792", "12672", "-68608", "309376", "-1203840", "2917888", "5570816", "-163782656", "1636425728", "-12716052480", "86205304832", "-495644917760", "2289265803264", "-4004259037184", "-73881736609792", "1359174582304768" ]
[ "sign", "easy" ]
20
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009059.seq
ef6758532d87c22e6800633f37602e4f
A009060
Expansion of e.g.f. cos(sinh(x)*cos(x)), even terms only.
[ "1", "-1", "9", "-57", "497", "-9169", "-299079", "7650615", "-160774303", "24228427487", "1725345708777", "-79802910103257", "-2815860329426863", "-984434470218538993", "-121507651305985736295", "12515845746505026745239" ]
[ "sign" ]
19
0
3
null
null
R. H. Hardin
2018-07-24T11:31:25
oeisdata/seq/A009/A009060.seq
35a3c4767fd45ba10fdba085e6c64ab8
A009061
Expansion of e.g.f. cos(sinh(x)*exp(x)).
[ "1", "0", "-1", "-6", "-27", "-100", "-237", "742", "18025", "194904", "1689671", "12483570", "72272013", "155614004", "-4305757029", "-101460169442", "-1561477983407", "-20064006763728", "-223375429298929", "-2048612121431958", "-11401251676320843", "95849085744834380" ]
[ "sign", "easy" ]
23
0
4
[ "A009061", "A009496", "A121868" ]
null
R. H. Hardin
2025-02-16T08:32:32
oeisdata/seq/A009/A009061.seq
c61e8cf64348a66fa40a01ac6007a304
A009062
Expansion of e.g.f.: cos(sinh(x)*log(1+x)).
[ "1", "0", "0", "0", "-12", "60", "-450", "2940", "-20720", "155232", "-1186920", "9474960", "-74648376", "552593184", "-3012161152", "-10103577120", "836086634240", "-22797582691456", "523741123519296", "-11502212537522304", "251821773466887808" ]
[ "sign", "easy" ]
18
0
5
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009062.seq
f9b0f2dfaeaaed8f1e84183380f109ab
A009063
Expansion of e.g.f. cos(sinh(x)*sin(x)) in powers of x^4.
[ "1", "-12", "2128", "-1586112", "3134810368", "-13146370501632", "101503034352652288", "-1310949029247657295872", "26429820982888342672703488", "-788858770066309331711165202432", "33443475995623429145380539537031168" ]
[ "sign" ]
13
0
2
null
null
R. H. Hardin
2018-07-24T20:17:35
oeisdata/seq/A009/A009063.seq
c233eb1a4a800077cd28329b01cf7068
A009064
Expansion of e.g.f. cos(sinh(x)/cos(x)), even powers only.
[ "1", "-1", "-15", "-297", "-6783", "-70609", "18558705", "4027228359", "727421677185", "134584692783455", "26232888936219249", "5245335359878123191", "971782758809341914369", "96545317222649153850767" ]
[ "sign" ]
14
0
3
null
null
R. H. Hardin
2018-07-24T21:22:15
oeisdata/seq/A009/A009064.seq
d162c40e779be320a75f009342b36697
A009065
Expansion of e.g.f. cos(tan(log(1+x))).
[ "1", "0", "-1", "3", "-18", "120", "-966", "8946", "-93748", "1094832", "-14078036", "197375420", "-2992213584", "48700300272", "-845573085072", "15571699693200", "-302493769715504", "6165508375224704", "-131129003401938832", "2892534929270217648" ]
[ "sign", "easy" ]
14
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009065.seq
f9362a7e3cb3b2a22cefad52eac298f8
A009066
Expansion of e.g.f. cos(tan(sin(x))), even terms only.
[ "1", "-1", "-3", "27", "1081", "3831", "-1567563", "-73024877", "4980721009", "1015258860783", "13245921859181", "-20750351796802549", "-3030717340459969623", "448360743236395743719", "256723841092587388040485" ]
[ "sign" ]
14
0
3
null
null
R. H. Hardin
2018-07-24T21:22:22
oeisdata/seq/A009/A009066.seq
651a1a1960057c0588a12a72a428c130
A009067
Expansion of e.g.f. cos(tan(sinh(x))), even terms only.
[ "1", "-1", "-11", "-253", "-9911", "-567449", "-42551299", "-3661191381", "-252072060911", "34332471915599", "34386811167577477", "19519494372343282899", "10751436426722565995609", "6281979864370292158301879" ]
[ "sign" ]
14
0
3
null
null
R. H. Hardin
2018-07-24T21:22:28
oeisdata/seq/A009/A009067.seq
757a5dc5bd33954b798e0a3efef1c345
A009068
Expansion of e.g.f. cos(tan(tan(x))), even terms only.
[ "1", "-1", "-15", "-513", "-31007", "-2881089", "-376412847", "-64825974593", "-13951231536191", "-3556538162237313", "-998391201911168335", "-261420586488162589057", "-14787500346745601332575", "86170769393986400590463039" ]
[ "sign" ]
14
0
3
null
null
R. H. Hardin
2018-07-24T21:22:35
oeisdata/seq/A009/A009068.seq
c4112033c890f1441a2ed33b819b0313
A009069
Expansion of e.g.f. cos(tan(tanh(x))), even terms only.
[ "1", "-1", "1", "47", "-1343", "8671", "2436545", "-249528945", "10176663169", "1606374108095", "-482969577637247", "59264468409177327", "4209524591120115521", "-4541227341778149686881", "1235175100383899185304129" ]
[ "sign" ]
14
0
4
null
null
R. H. Hardin
2018-07-24T21:22:42
oeisdata/seq/A009/A009069.seq
ff1a99e8cb55dc1c523ca4b78910a834
A009070
Ordered sides of Pythagorean triangles.
[ "3", "4", "5", "5", "6", "7", "8", "8", "9", "9", "10", "10", "11", "12", "12", "12", "12", "13", "13", "14", "15", "15", "15", "15", "15", "16", "16", "16", "17", "17", "18", "18", "19", "20", "20", "20", "20", "20", "21", "21", "21", "21", "22", "23", "24", "24", "24", "24", "24", "24", "24", "25", "25", "25", "25", "26", "26", "27", "27", "27", "28", "28", "28", "28", "29", "29", "30", "30", "30", "30", "30", "31", "32", "32", "32" ]
[ "nonn" ]
10
1
1
[ "A009000", "A009004", "A009012", "A009041", "A009070" ]
null
David W. Wilson
2018-04-19T17:35:47
oeisdata/seq/A009/A009070.seq
a20ec590b0693c446a1b626bfbc08dbd
A009071
Expansion of e.g.f. cos(tan(x))*x, odd terms only.
[ "1", "-3", "-35", "-679", "-18567", "-587499", "-9780459", "2502478065", "742659420913", "178572619407021", "44455465546363725", "12065488445289701385", "3615507259471920747625", "1195750896202918862106309", "433676146678880946251117189", "170620060022539628512713371809" ]
[ "sign" ]
18
0
2
null
null
R. H. Hardin
2018-07-24T21:22:49
oeisdata/seq/A009/A009071.seq
f730abb2bc151175a6ddd41c01b4dcf1
A009072
Expansion of e.g.f. cos(tan(x))/cos(x), even-indexed terms only.
[ "1", "0", "-8", "-216", "-7552", "-349568", "-20281216", "-1350879232", "-84211707904", "286327484416", "2529465981566976", "1100934401707376640", "421697958276604264448", "165461414536859529248768", "69271409331127446269067264" ]
[ "sign" ]
18
0
3
null
null
R. H. Hardin
2024-03-28T21:57:04
oeisdata/seq/A009/A009072.seq
ca3e05e4dd40f9e94a6afd5cb01083a8
A009073
Expansion of e.g.f. cos(tan(x))/cosh(x), even terms only.
[ "1", "-2", "4", "-128", "1296", "-85600", "4372160", "-148860416", "54261590272", "1474575037952", "1579094994228224", "145025202842173440", "87575771555229601792", "13290672132247757398016", "8077796113026531668901888" ]
[ "sign" ]
16
0
2
null
null
R. H. Hardin
2018-07-24T21:22:56
oeisdata/seq/A009/A009073.seq
bb37d6aee84c7c4213ae3a5a75bd9969
A009074
Expansion of e.g.f. cos(tan(x))/exp(x).
[ "1", "-1", "0", "2", "-12", "44", "-216", "944", "-5296", "27632", "-168128", "975072", "-5391680", "27882048", "38412672", "-1986004224", "61881368832", "-850359527680", "16576603568128", "-222801125934592", "4120672559178752", "-57863671042155520" ]
[ "sign", "easy" ]
15
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009074.seq
a91bb45c0ebbee63879b13ebe133ab4f
A009075
Expansion of e.g.f. cos(tan(x)*cosh(x)), even terms only.
[ "1", "-1", "-19", "-397", "-7943", "64551", "43466469", "7570028763", "1224976528753", "203222727578703", "33945910273599581", "5001827577751516739", "201232322297192328041", "-395596937210124802877833" ]
[ "sign" ]
19
0
3
null
null
R. H. Hardin
2024-01-26T04:59:53
oeisdata/seq/A009/A009075.seq
6c371bb899b1981f884c5ce1888b511a
A009076
Expansion of e.g.f. cos(tan(x)*exp(x)).
[ "1", "0", "-1", "-6", "-31", "-140", "-577", "-1498", "6785", "192840", "2667711", "31783730", "353106657", "3771795196", "38270910975", "356214219678", "2639000258561", "4515406498320", "-420731049845121", "-13553517751217174", "-318084517098105631" ]
[ "sign", "easy" ]
15
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009076.seq
5a103f3df08e44cb91aeb1c349cafda0
A009077
Expansion of e.g.f. cos(tan(x)*log(1+x)).
[ "1", "0", "0", "0", "-12", "60", "-570", "3780", "-33600", "266112", "-2452200", "21323280", "-195333336", "1587135264", "-9944442144", "-30963922080", "3059476293120", "-90038301262976", "2195425718875200", "-50367095018001792", "1140534839454383488" ]
[ "sign", "easy" ]
14
0
5
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009077.seq
037c4af5426c268872f21dce5c86bf5b
A009078
Expansion of e.g.f. cos(tan(x)*sin(x)) (even powers only).
[ "1", "0", "-12", "-120", "-2352", "-75840", "-1649472", "118634880", "41344643328", "9528901232640", "2213829515240448", "559192086549719040", "156367986602421669888", "48476425507418343751680", "16569615994864645076533248" ]
[ "sign" ]
21
0
3
null
null
R. H. Hardin
2018-07-24T21:23:36
oeisdata/seq/A009/A009078.seq
d27d7cb8f6c80b8436190a0e9a91fff9
A009079
Expansion of e.g.f. cos(tan(x)*sinh(x)), even powers only.
[ "1", "0", "-12", "-360", "-11312", "-342720", "1391808", "3011648640", "712998408448", "151782346782720", "33053467644945408", "7470073537438955520", "1689905119837405401088", "334766606514085190615040", "19605053176568811703615488", "-43798309867240412782195998720" ]
[ "sign" ]
22
0
3
null
null
R. H. Hardin
2018-07-25T08:16:25
oeisdata/seq/A009/A009079.seq
2092c5b9b3fa16ae128b7772e7cd3d2b
A009080
Expansion of e.g.f. cos(x*tan(x)), even terms only.
[ "1", "0", "-12", "-240", "-5936", "-155520", "-65472", "981903104", "223580862720", "46255608778752", "10060678641587200", "2368138744630923264", "601490101481648443392", "161192778898870464512000", "43208403753541588946141184" ]
[ "sign" ]
16
0
3
null
null
R. H. Hardin
2018-07-24T21:23:42
oeisdata/seq/A009/A009080.seq
ef6209608acf3e2fcc231880e27b6874
A009081
E.g.f. is cos(tan(x)/cos(x)), coefficients of even powers of x.
[ "1", "-1", "-19", "-517", "-18023", "-587529", "19183749", "12219870323", "3379214470193", "883981857320943", "238930492488456221", "66829754023676225259", "18410558239851140719561", "4167711609283156286652647", "-82954815883633697917244747", "-1284116651310135986426544039581" ]
[ "sign" ]
25
0
3
null
null
R. H. Hardin
2017-04-12T23:09:01
oeisdata/seq/A009/A009081.seq
04ce9774ad1c1c137d53c58fd6cf3269
A009082
Expansion of e.g.f. cos(tan(x)/cosh(x)), even terms only.
[ "1", "-1", "5", "-157", "3817", "-257049", "15886125", "-1844058101", "218349214545", "-38729647296945", "7468216325125589", "-1882371895493492429", "533348579359954590009", "-181834605583994802568393" ]
[ "sign" ]
14
0
3
null
null
R. H. Hardin
2018-07-24T21:23:49
oeisdata/seq/A009/A009082.seq
78a04a17071c056ed1cbdd367493a5f8
A009083
Expansion of e.g.f. cos(tan(x)^2) (even powers only).
[ "1", "0", "-12", "-480", "-22512", "-1224960", "-61017792", "1438993920", "1844639547648", "677206700482560", "225542012911531008", "76252348319434383360", "26581103125260630233088", "9309180001030233433374720" ]
[ "sign" ]
17
0
3
null
null
R. H. Hardin
2018-07-24T21:23:55
oeisdata/seq/A009/A009083.seq
a4fb62d0bbd08ef5edcbb7b4969a6b55
A009084
Expansion of e.g.f.: cos(tanh(log(1+x))).
[ "1", "0", "-1", "3", "-2", "-40", "314", "-1134", "-3044", "87408", "-733636", "1835020", "43592176", "-792796368", "6272579312", "14019198480", "-1257528653744", "20065121039744", "-124527163941136", "-2075494412476368", "75585686698926496", "-1110720454454795520" ]
[ "sign", "easy" ]
19
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009084.seq
dffc42f949463a2c189de1eb29c57f2d
A009085
Expansion of e.g.f. cos(tanh(sin(x))), even powers only.
[ "1", "-1", "13", "-373", "19097", "-1522409", "174263717", "-27072485469", "5477315064625", "-1398343023229393", "439386703590146365", "-166541598232670049093", "74891796652158938855881", "-39404384075265527597485241" ]
[ "sign" ]
21
0
3
null
null
R. H. Hardin
2018-07-26T07:54:13
oeisdata/seq/A009/A009085.seq
eb707950c5c73be7d63e48af6ad7fabe
A009086
Expansion of e.g.f. cos(tanh(tan(x))), even powers only.
[ "1", "-1", "1", "47", "449", "-18209", "-1441087", "-41192817", "2660018305", "460752070079", "21450325749889", "-1057483104728337", "760394598152560705", "506532040802152000159", "99674104328764912612673" ]
[ "sign" ]
18
0
4
null
null
R. H. Hardin
2018-07-25T08:16:38
oeisdata/seq/A009/A009086.seq
71bdc59dc54276615838409ff6f93a89
A009087
Numbers whose number of divisors is prime (i.e., numbers of the form p^(q-1) for primes p,q).
[ "2", "3", "4", "5", "7", "9", "11", "13", "16", "17", "19", "23", "25", "29", "31", "37", "41", "43", "47", "49", "53", "59", "61", "64", "67", "71", "73", "79", "81", "83", "89", "97", "101", "103", "107", "109", "113", "121", "127", "131", "137", "139", "149", "151", "157", "163", "167", "169", "173", "179", "181", "191", "193", "197", "199", "211", "223", "227", "229", "233", "239" ]
[ "nice", "nonn", "easy" ]
40
1
1
[ "A000961", "A009087", "A023194", "A036454", "A203967" ]
null
Simon Colton (simonco(AT)cs.york.ac.uk)
2025-02-22T12:08:18
oeisdata/seq/A009/A009087.seq
004d8a45ce95b6821a668db565b6ac2f
A009088
Expansion of e.g.f. x*cos(tanh(x)), odd powers only.
[ "1", "-3", "45", "-1239", "54873", "-3577739", "322495173", "-38370542175", "5817952885169", "-1093812528874387", "249472828725529437", "-67807763939709678951", "21642089202188444732425", "-8010884242566625383028251" ]
[ "sign" ]
25
0
2
null
null
R. H. Hardin
2018-07-30T00:39:09
oeisdata/seq/A009/A009088.seq
1b36e43b1ca6dfe6cbfbab8a2fa8ae4b
A009089
Expansion of e.g.f. cos(tanh(x))/cos(x), even powers only.
[ "1", "0", "8", "-56", "3968", "-133248", "13993088", "-1139191808", "178943504384", "-26439024316416", "5943319707680768", "-1368130407134953472", "421233393478948782080", "-137934416762714295631872", "56032481949750675250085888" ]
[ "sign" ]
20
0
3
null
null
R. H. Hardin
2018-07-25T06:15:38
oeisdata/seq/A009/A009089.seq
0acda2de1d424fc3aa3385c3e2963610
A009090
Expansion of e.g.f. cos(tanh(x))/exp(x).
[ "1", "-1", "0", "2", "4", "-36", "-56", "944", "1744", "-41104", "-86208", "2650592", "6199744", "-237023424", "-608357504", "28021573376", "77889982720", "-4225816615168", "-12588540708864", "790713657219584", "2503565961032704", "-179579770991391744" ]
[ "sign", "easy" ]
16
0
4
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009090.seq
db913613db79a318aa07daeb4a6e46a7
A009091
Expansion of e.g.f. cos(tanh(x)*cos(x)), even powers only.
[ "1", "-1", "21", "-597", "26537", "-1834249", "180938109", "-23781199197", "3989919982673", "-830092069266577", "209479116176732901", "-62986349633232396261", "22231865269167169440761", "-9096170536950779556167833" ]
[ "sign" ]
19
0
3
null
null
R. H. Hardin
2018-07-26T08:03:23
oeisdata/seq/A009/A009091.seq
b91a5ebb3e6f09dcb5bfe8db41ed4715
A009092
Expansion of e.g.f. cos(tanh(x)*exp(x)).
[ "1", "0", "-1", "-6", "-15", "20", "303", "742", "-2975", "-17784", "101471", "1089330", "-4112559", "-109689892", "-175956081", "10257283678", "62492991169", "-1187272882032", "-14383393311553", "159864567511530", "3401397735742641", "-22534114976850652" ]
[ "sign", "easy" ]
24
0
4
null
null
R. H. Hardin
2023-12-31T15:51:25
oeisdata/seq/A009/A009092.seq
469d5590b1fb04394d6f669e05b8e843
A009093
Expansion of e.g.f. cos(tanh(x)*log(1+x)).
[ "1", "0", "0", "0", "-12", "60", "-90", "420", "-8960", "64512", "-299880", "3709200", "-52709976", "480109344", "-4993564576", "83895608160", "-1246488056320", "15764924418944", "-251656080793536", "4849396180905600", "-84861914800295552", "1455466222530055680" ]
[ "sign", "easy" ]
15
0
5
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009093.seq
98acd934b8f855a0031f52ee0caeaa98
A009094
Expansion of e.g.f. cos(tanh(x)*tan(x)) (only powers that are multiples of 4).
[ "1", "-12", "-4592", "-6274752", "18138366208", "2332645761266688", "202540305420145266688", "24977439274944176331767808", "4480212151308993274762821173248", "1107507319145672023044777103840247808", "336310686770623540666061200154740824997888" ]
[ "sign" ]
21
0
2
null
null
R. H. Hardin
2018-07-26T07:44:24
oeisdata/seq/A009/A009094.seq
fae94988f37ddd2dbe818107d18d25f8
A009095
Expansion of e.g.f. cos(tanh(x)/cos(x)), even powers only.
[ "1", "-1", "-3", "-117", "-903", "-111529", "687093", "-320199453", "44530596081", "-254346923089", "2006766293627373", "141849542553657147", "144420752722329270633", "17706925736601628695047", "16789499049770600380859877" ]
[ "sign" ]
16
0
3
null
null
R. H. Hardin
2018-07-26T08:03:39
oeisdata/seq/A009/A009095.seq
26da6ebd8808047e8cda2cd210fd67e0
A009096
Ordered perimeters of Pythagorean triangles.
[ "12", "24", "30", "36", "40", "48", "56", "60", "60", "70", "72", "80", "84", "84", "90", "90", "96", "108", "112", "120", "120", "120", "126", "132", "132", "140", "144", "144", "150", "154", "156", "160", "168", "168", "168", "176", "180", "180", "180", "182", "192", "198", "200", "204", "208", "210", "210", "216", "220", "224", "228", "234", "240", "240", "240", "240", "252", "252" ]
[ "nonn" ]
10
1
1
null
null
David W. Wilson
2016-07-07T23:48:44
oeisdata/seq/A009/A009096.seq
ff6281b50f1d5e1f68a7621ec6ab7b99
A009097
Expansion of e.g.f. cos(x)*cos(log(1+x)).
[ "1", "0", "-2", "3", "-3", "10", "-56", "315", "-1971", "13788", "-105246", "857615", "-7266223", "61296222", "-465353292", "1982748495", "36246192441", "-1600097656520", "43901543199046", "-1078930450441413", "25757481055625541", "-615789512284527630" ]
[ "sign", "easy" ]
23
0
3
null
null
R. H. Hardin
2022-09-08T08:44:37
oeisdata/seq/A009/A009097.seq
3eea011bcf61f1538abc66702deaf0c7
A009098
Expansion of e.g.f. cos(x)*cos(sinh(x)), even powers only.
[ "1", "-2", "4", "32", "-48", "-5600", "-85568", "533504", "85827840", "3149702656", "27282224128", "-5424499154944", "-496815684169728", "-22408107489910784", "247218592921600000", "170684586701783564288", "20039831043212444762112" ]
[ "sign" ]
19
0
2
null
null
R. H. Hardin
2018-07-26T08:04:01
oeisdata/seq/A009/A009098.seq
9d428efd8bbb20dd1e5e988af0ef8cbb
A009099
Expansion of e.g.f. cos(x)*cos(tan(x)), even powers only.
[ "1", "-2", "0", "-8", "192", "20480", "1837696", "187743488", "22698672128", "3236847570944", "536307107184640", "101121059849109504", "21095686709291679744", "4655115962946721611776", "983762698552391462027264" ]
[ "sign" ]
16
0
2
null
null
R. H. Hardin
2018-07-26T08:04:12
oeisdata/seq/A009/A009099.seq
69c90cba2c73499ce341d4cb121e45ff
A009100
Expansion of e.g.f. cos(x)*cos(tanh(x)), even powers only.
[ "1", "-2", "16", "-328", "11712", "-638720", "49459840", "-5159926528", "697030680576", "-118233272496128", "24578235697610752", "-6139851821419921408", "1813615341438397218816", "-624948457889265099014144" ]
[ "sign" ]
19
0
2
null
null
R. H. Hardin
2018-07-26T08:04:18
oeisdata/seq/A009/A009100.seq
d5a757193ee3cb7e4b2d7aa2c8583203