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%I #4 Dec 16 2019 14:25:43
%S 1,2,7,24,129,840,5265,40320,434385,3900960,40809825,558835200,
%T 6335076825,91070179200,1641957141825,20922789888000,359796258446625,
%U 7663952552256000,122832552380162625,2615369658789888000,62315614994643635625
%N Expansion of e.g.f. Sum_{k>=1} arcsin(x^k).
%F a(n) = n! * Sum_{d|n, d odd} ((d - 2)!!)^2 / d!.
%t nmax = 21; CoefficientList[Series[Sum[ArcSin[x^k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%t Table[n! DivisorSum[n, ((# - 2)!!)^2/#! &, OddQ[#] &], {n, 1, 21}]
%Y Cf. A001818, A176473, A184877, A330254, A330505.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Dec 16 2019
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