A385471 - OEIS

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

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OFFSET

0,2

LINKS

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

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).

a(n) ~ sqrt(Pi) * 2^(5/2) * (exp(2/3) + 1)^(n-1) * n^(n + 1/2) / (3 * exp(n - 2/3) * (exp(2/3) - 1)^(n+1)). - Vaclav Kotesovec, Feb 04 2026

MATHEMATICA

nmax = 20; CoefficientList[Series[1/(1 - (3/2) * Log[(1+x)/(1-x)]), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Feb 04 2026 *)