A385376 Expansion of e.g.f. 1/(1 - 2 * arcsin(x))^(1/2).

1, 1, 3, 16, 117, 1104, 12687, 172320, 2698377, 47880960, 949330203, 20801387520, 499149710205, 13018307696640, 366673138800615, 11092295404707840, 358685609335654545, 12346621534211604480, 450741642786156589875, 17395372731952677519360, 707614393333663454022405

Offset: 0

Author

Seiichi Manyama, Jun 27 2025

Keywords

• nonn

Crossrefs

Cf. A189780, A385377.

Cf. A001147, A385343, A385346.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-2*asin(x))^(1/2)))

Formula

a(n) = Sum_{k=0..n} A001147(k) * A385343(n,k).

a(n) ~ sqrt(cos(1/2)) * n^n / (exp(n) * sin(1/2)^(n + 1/2)). - Vaclav Kotesovec, Jun 27 2025