A385377 Expansion of e.g.f. 1/(1 - 3 * arcsin(x))^(1/3).

1, 1, 4, 29, 296, 3929, 64096, 1241437, 27834496, 709117073, 20232018944, 639064971293, 22138797783040, 834595012185193, 34013250713804800, 1490126154034917917, 69836524615835156480, 3486395656135414573985, 184703404516197170544640, 10349751400296465164293405

Offset: 0

Author

Seiichi Manyama, Jun 27 2025

Keywords

• nonn

Crossrefs

Cf. A189780, A385376.

Cf. A007559, A385343, A385347.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*asin(x))^(1/3)))

Formula

a(n) = Sum_{k=0..n} A007559(k) * A385343(n,k).

a(n) ~ sqrt(2*Pi) * cos(1/3)^(1/3) * n^(n - 1/6) / (Gamma(1/3) * 3^(1/3) * exp(n) * sin(1/3)^(n + 1/3)). - Vaclav Kotesovec, Jun 27 2025