A302605 a(n) = n! * [x^n] exp(n*x)*arcsin(x).

0, 1, 4, 28, 272, 3384, 51300, 917064, 18884672, 440168832, 11454902500, 329208395264, 10355322975120, 353851897861760, 13052503620917124, 516917167506777600, 21875427250996723968, 985164766018898243584, 47043119138733155306052, 2374168079889664129576960

Offset: 0

Author

Ilya Gutkovskiy, Apr 10 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..384
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A001818, A115416, A291482, A293191, A302583, A302584, A302585, A302586, A302587, A302606, A302608, A302609.

Programs

Mathematica

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

Formula

a(n) = Sum_{k=1..n} binomial(n,k)*(k-2)!!^2*n^(n-k)*(1-(-1)^k)/2. - Fabian Pereyra, Oct 05 2024