A385420 Expansion of e.g.f. 1/(1 - arcsinh(3*x))^(1/3).

1, 1, 4, 19, 136, 1849, 28576, 383347, 6054016, 162756433, 4512553984, 94198960723, 2151597168640, 94600222614793, 3958651982848000, 103976698299157747, 2765446240371834880, 197818347558313860385, 11750108763413970288640, 335351034570439348695955

Offset: 0

Author

Seiichi Manyama, Jun 28 2025

Keywords

• sign

Comments

a(28) = -1984619795429736510626124031150165852160.

Crossrefs

Cf. A296675, A385419.

Cf. A007559, A385372, A385343, A385422.

Programs

PARI

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

Formula

E.g.f.: 1/(1 - log(3*x + sqrt(9*x^2 + 1)))^(1/3).

a(n) = Sum_{k=0..n} A007559(k) * (3*i)^(n-k) * A385343(n,k), where i is the imaginary unit.