This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330512 #4 Dec 17 2019 08:41:02
%S A330512 1,2,5,24,129,600,4815,40320,313425,3900960,39023775,399168000,
%T A330512 6335076825,83286403200,1169542749375,20922789888000,359796258446625,
%U A330512 5529827983680000,120457648437501375,2615369658789888000,40723609672075955625
%N A330512 Expansion of e.g.f. Sum_{k>=1} arcsinh(x^k).
%F A330512 E.g.f.: Sum_{k>=1} log(x^k + sqrt(1 + x^(2*k))).
%F A330512 a(n) = n! * Sum_{d|n, d odd} (-1)^((d - 1)/2) * ((d - 2)!!)^2 / d!.
%t A330512 nmax = 21; CoefficientList[Series[Sum[ArcSinh[x^k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%t A330512 Table[n! DivisorSum[n, (-1)^((# - 1)/2) ((# - 2)!!)^2/#! &, OddQ[#] &], {n, 1, 21}]
%Y A330512 Cf. A001818, A330254, A330505, A330506.
%K A330512 nonn
%O A330512 1,2
%A A330512 _Ilya Gutkovskiy_, Dec 16 2019