A385469 Expansion of e.g.f. 1/(1 - 3 * arctanh(x))^(1/3).

1, 1, 4, 30, 312, 4224, 70176, 1384032, 31590912, 819254016, 23792039424, 764912590848, 26970073390080, 1034798724320256, 42921327875788800, 1913760046417508352, 91281373260924026880, 4637755280044146032640, 250054580636566927441920, 14259891701316651909120000

Offset

0,3

Links

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

Formula

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

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

a(n) ~ sqrt(Pi) * 2^(7/6) * (exp(2/3) + 1)^(n - 1/3) * n^(n - 1/6) / (3^(1/3) * Gamma(1/3) * exp(n - 2/9) * (exp(2/3) - 1)^(n + 1/3)). - Vaclav Kotesovec, Sep 30 2025

Prog

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

Crossrefs

Cf. A296676, A385468.

Cf. A007559, A111594.

Sequence in context: A239841 A145348 A052574 * A158834 A139086 A382840

Adjacent sequences: A385466 A385467 A385468 * A385470 A385471 A385472

Keyword

nonn

Author

Seiichi Manyama, Jun 30 2025

Status

approved