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]!
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}]
A330535
Expansion of e.g.f. Product_{k>=1} 1 / (1 - arcsinh(x^k)).
Original entry on oeis.org
1, 1, 4, 17, 112, 769, 7088, 66387, 763600, 9164721, 126474672, 1820139771, 29458146408, 494179557897, 9100332756552, 174762729699459, 3612983961103776, 77711328568772193, 1784695351000035744, 42494646959739633771
Offset: 0
-
nmax = 19; CoefficientList[Series[Product[1/(1 - ArcSinh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[Exp[Sum[Sum[ArcSinh[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
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 1-5 of 5 results.