A385468 Expansion of e.g.f. 1/(1 - 2 * arctanh(x))^(1/2).

1, 1, 3, 17, 129, 1269, 15147, 213765, 3475329, 64020585, 1317472563, 29960707545, 746086414785, 20192521440285, 590166330458715, 18525204423695565, 621571306435103745, 22199954036873457105, 840913892465144800995, 33672216851574639900705

Offset: 0

Author

Seiichi Manyama, Jun 30 2025

Keywords

• nonn
• easy

Crossrefs

Cf. A296676, A385469.

Cf. A001147, A111594, A385376.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*atanh(x))^(1/2)))

Formula

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

a(n) = Sum_{k=0..n} A001147(k) * A111594(n,k).

a(n) ~ 2 * (exp(1) + 1)^(n - 1/2) * n^n / (exp(n - 1/2) * (exp(1) - 1)^(n + 1/2)). - Vaclav Kotesovec, Jun 30 2025