A385346 Expansion of e.g.f. 1/(1 - 2 * arcsin(x)).

1, 2, 8, 50, 416, 4338, 54272, 792402, 13221888, 248206818, 5177131008, 118784695218, 2973171646464, 80619877999698, 2354230063005696, 73657841729314002, 2458203242895507456, 87165684035402711490, 3272629788196529504256, 129696816160868956695090

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} 2^k * k! * A385343(n,k).

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*asin(x))))

Crossrefs

Cf. A189780, A385347.

Cf. A385343.

Sequence in context: A121677 A120956 A000557 * A193352 A002801 A322738

Adjacent sequences: A385343 A385344 A385345 * A385347 A385348 A385349

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 26 2025

Status

approved