A385473 - OEIS

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

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

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).

a(n) ~ sqrt(Pi) * 2^(7/6) * 3^n * (exp(2) + 1)^(n - 1/3) * n^(n - 1/6) / (Gamma(1/3) * exp(n - 2/3) * (exp(2) - 1)^(n + 1/3)). - Vaclav Kotesovec, Sep 30 2025

PROG

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

CROSSREFS

Cf. A296676, A385472.

Cf. A007559, A111594.

Sequence in context: A222098 A197131 A235132 * A236956 A113264 A264717

Adjacent sequences: A385470 A385471 A385472 * A385474 A385475 A385476

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jun 30 2025

STATUS

approved