A330506 Expansion of e.g.f. Sum_{k>=1} arcsin(x^k).

1, 2, 7, 24, 129, 840, 5265, 40320, 434385, 3900960, 40809825, 558835200, 6335076825, 91070179200, 1641957141825, 20922789888000, 359796258446625, 7663952552256000, 122832552380162625, 2615369658789888000, 62315614994643635625

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

a(n) = n! * Sum_{d|n, d odd} ((d - 2)!!)^2 / d!.

Mathematica

nmax = 21; CoefficientList[Series[Sum[ArcSin[x^k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! DivisorSum[n, ((# - 2)!!)^2/#! &, OddQ[#] &], {n, 1, 21}]

Crossrefs

Cf. A001818, A176473, A184877, A330254, A330505.

Sequence in context: A150451 A150452 A330254 * A236422 A013204 A013209

Adjacent sequences: A330503 A330504 A330505 * A330507 A330508 A330509

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 16 2019

Status

approved