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%I #12 Nov 21 2020 21:37:39
%S 1,1,4,30,320,4420,74880,1502200,34816000,915267600,26907545600,
%T 874679634400,31150846771200,1206169954600000,50449154129920000,
%U 2266730426366640000,108883850653859840000,5568313898902866592000,302047359993635143680000,17321727685903810436800000
%N a(n) = n! * [x^n] exp(n*arcsin(x)).
%F a(n) ~ 2^((n-1)/2) * exp(Pi*n/4 - n) * n^n. - _Vaclav Kotesovec_, Oct 02 2017
%F a(0) = a(1) = 1; a(n) = 2 * Sum_{k=1..n-1} binomial(n,k) * a(k) * a(n-k-1). - _Ilya Gutkovskiy_, Nov 21 2020
%t Table[n! SeriesCoefficient[Exp[n ArcSin[x]], {x, 0, n}], {n, 0, 19}]
%Y Cf. A002866, A006228, A166741.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Oct 02 2017
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