A270294
E.g.f.: Product_{k>=1} (1 + sinh(x^k)).
Original entry on oeis.org
1, 1, 2, 13, 48, 381, 3120, 26923, 255696, 3158137, 40008240, 519979791, 7942304040, 122856625477, 2131578891624, 39647280625891, 750423985762080, 15134456564892273, 334165931467245216, 7422976578858122647, 177254117413133743800, 4454974632071621551741
Offset: 0
-
nmax = 25; Range[0, nmax]!*CoefficientList[Series[Product[1+Sinh[x^k], {k, 1, nmax}], {x, 0, nmax}], x]
A270662
E.g.f.: Product_{k>=1} (1 + sin(x^k)).
Original entry on oeis.org
1, 1, 2, 11, 48, 341, 2640, 23561, 228816, 2674153, 32749200, 440019469, 6504919080, 102077649805, 1724124159576, 31359633592769, 596774321099040, 12048020039472209, 259300490127149664, 5798531237450331797, 136619813565630980280, 3380131718416134261301
Offset: 0
-
nmax = 25; Range[0, nmax]! * CoefficientList[Series[Product[1+Sin[x^k], {k, 1, nmax}], {x, 0, nmax}], x]
A270663
E.g.f.: Product_{k>=1} cos(x^k) [even terms only].
Original entry on oeis.org
1, -1, -11, -181, -9239, -148681, -49402979, 6471717251, 42662277841, 658656817939439, 133531458273294661, 168943525289665105979, 19015164932231993967289, 62294481438650615377602599, 18546969159687034895328945901, 27398539855607539080934584895859
Offset: 0
-
nmax = 20; Table[(Range[0, 2*nmax]! * CoefficientList[Series[Product[Cos[x^k], {k, 1, 2*nmax}], {x, 0, 2*nmax}], x])[[2*n + 1]], {n, 0, nmax}]
A330514
Expansion of e.g.f. Product_{k>=1} 1 / (1 - sin(x^k)).
Original entry on oeis.org
1, 1, 4, 17, 112, 761, 6992, 65267, 749264, 8952097, 123035312, 1765177435, 28465913320, 475981018033, 8737060100680, 167186734385795, 3446660462332576, 73894280818392641, 1691674707666258848, 40160865451008020651, 1009283508170762388536
Offset: 0
Cf.
A000111,
A203716,
A229263,
A270294,
A270662,
A270663,
A270664,
A270665,
A270666,
A330515,
A330516,
A330517.
-
nmax = 20; CoefficientList[Series[Product[1/(1 - Sin[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A330515
Expansion of e.g.f. Product_{k>=1} 1 / (1 - sinh(x^k)).
Original entry on oeis.org
1, 1, 4, 19, 128, 921, 8912, 87109, 1045200, 13195681, 188639312, 2837096637, 47976425576, 837845855185, 16039578298200, 321739841159317, 6911395312352672, 154749452408120385, 3696709758990757856, 91546190261460505453, 2397650607409036823352
Offset: 0
Cf.
A006154,
A203716,
A229263,
A270294,
A270662,
A270663,
A270664,
A270665,
A270666,
A330514,
A330516,
A330517.
-
nmax = 20; CoefficientList[Series[Product[1/(1 - Sinh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A330516
Expansion of e.g.f. Product_{k>=1} sec(x^k) (even powers only).
Original entry on oeis.org
1, 1, 17, 601, 44225, 4589041, 781157585, 162882093193, 48519650017025, 17223202538504161, 7898449818361655825, 4193448664548573675961, 2779065418077990268214465, 2061320859693223620523895761, 1836094285018667246330440863185
Offset: 0
Cf.
A000364,
A203716,
A229263,
A270294,
A270662,
A270663,
A270664,
A270665,
A270666,
A330514,
A330515,
A330517.
-
nmax = 14; Table[(CoefficientList[Series[Product[Sec[x^k], {k, 1, nmax}], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
A330517
Expansion of e.g.f. Product_{k>=1} sech(x^k) (even powers only).
Original entry on oeis.org
1, -1, -7, -241, -4495, -652801, -15004375, -7047990769, 1597056262625, -360304327144321, 286464442762907225, 560117092794518159, 78257061390674957994065, 5684812583023438995911039, 45666128878264725133259682185
Offset: 0
Cf.
A000364,
A203716,
A229263,
A270294,
A270662,
A270663,
A270664,
A270665,
A270666,
A330514,
A330515,
A330516.
-
nmax = 14; Table[(CoefficientList[Series[Product[Sech[x^k], {k, 1, nmax}], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
A330518
Expansion of e.g.f. Product_{k>=1} (sec(x^k) + tan(x^k)).
Original entry on oeis.org
1, 1, 3, 14, 77, 536, 4471, 41474, 437737, 5206120, 67098091, 944705662, 14495605277, 237203399044, 4162492013135, 78089687760842, 1545654292223825, 32385137447167280, 716473190874986323, 16611710217097325366, 404119023609893926405
Offset: 0
Cf.
A000111,
A203716,
A229263,
A270294,
A270662,
A270663,
A270664,
A270665,
A270666,
A330514,
A330515,
A330516,
A330517.
-
nmax = 20; CoefficientList[Series[Product[(Sec[x^k] + Tan[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Showing 1-8 of 8 results.