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%I #36 May 23 2022 09:12:48
%S 1,0,1,-4,29,-124,1583,-17088,124553,-1152816,20127867,-262838016,
%T 3978820221,-48595514304,914656587063,-24441484099584,370244721585681,
%U -5884988565575424,162968423791332339,-3855257807841017856,82014901819948738629,-1934570487417807744000,58311771938510122952559
%N Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + arcsin(x).
%F E.g.f.: Sum_{k>=1} A067856(k) * log(1 + arcsin(x^k)) / k.
%t b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[c[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; c[n_] := c[n] = Mod[n, 2] (n - 2)!!/(n (n - 1)!!) - b[n, n - 1]; a[n_] := n! c[n]; Table[a[n], {n, 1, 23}]
%Y Cf. A001818, A067856, A353818, A353913, A354115, A354171, A354274, A354275, A354276.
%K sign
%O 1,4
%A _Ilya Gutkovskiy_, May 22 2022
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