A270670
E.g.f.: Product_{k>=1} (1 + k*sinh(x^k)).
Original entry on oeis.org
1, 1, 4, 31, 168, 1841, 18600, 221845, 2655408, 44969041, 703172880, 11894018621, 231354830520, 4504644624793, 100890401218152, 2370351246834901, 55456622199548640, 1400307612079837985, 39002429830457675808, 1058964187034314179181, 32049467535091477285800
Offset: 0
-
nn = 25; Range[0, nn]! * CoefficientList[Series[Product[1+k*Sinh[x^k], {k, 1, nn}], {x, 0, nn}], x]
A330540
Expansion of e.g.f. Product_{k>=1} (1 + arcsinh(x^k)).
Original entry on oeis.org
1, 1, 2, 11, 48, 349, 2640, 23673, 231504, 2693241, 33313680, 446104845, 6572693160, 103319528805, 1750718151000, 31865325610545, 607019625223200, 12253084499034225, 263721891513921120, 5900460781451357205, 139338570648068278200
Offset: 0
-
nmax = 20; CoefficientList[Series[Product[(1 + ArcSinh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Exp[Sum[Sum[(-1)^(d + 1) 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]!