A385473 Expansion of e.g.f. 1/(1 - arctanh(3*x))^(1/3).

1, 1, 4, 46, 568, 10624, 218656, 5702752, 163568128, 5497133824, 201702168064, 8319367856128, 371416377318400, 18185429803469824, 955872746109276160, 54228988018125125632, 3278679608280623841280, 211600457615794941460480, 14461966051190623712051200

Offset: 0

Author

Seiichi Manyama, Jun 30 2025

Keywords

• nonn
• easy

Crossrefs

Cf. A296676, A385472.

Cf. A007559, A111594.

Programs

PARI

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

Formula

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

a(n) = Sum_{k=0..n} A007559(k) * 3^(n-k) * A111594(n,k).