A293191 a(n) = n! * [x^n] exp(n*arcsin(x)).

1, 1, 4, 30, 320, 4420, 74880, 1502200, 34816000, 915267600, 26907545600, 874679634400, 31150846771200, 1206169954600000, 50449154129920000, 2266730426366640000, 108883850653859840000, 5568313898902866592000, 302047359993635143680000, 17321727685903810436800000

Offset: 0

Author

Ilya Gutkovskiy, Oct 02 2017

Keywords

• nonn

Crossrefs

Cf. A002866, A006228, A166741.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[n ArcSin[x]], {x, 0, n}], {n, 0, 19}]

Formula

a(n) ~ 2^((n-1)/2) * exp(Pi*n/4 - n) * n^n. - Vaclav Kotesovec, Oct 02 2017

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