A385471 Expansion of e.g.f. 1/(1 - 3 * arctanh(x)).

1, 3, 18, 168, 2088, 32472, 605952, 13192848, 328268160, 9189103104, 285808290048, 9778434400512, 364965976571904, 14756982055363584, 642580290860378112, 29979230177385750528, 1491908801018949697536, 78884742832151951278080, 4416389166601900315901952

Offset: 0

Author

Seiichi Manyama, Jun 30 2025

Keywords

• nonn
• easy

Crossrefs

Cf. A296676, A385470.

Cf. A111594, A385469.

Programs

PARI

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A385469.

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

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