A385472 Expansion of e.g.f. 1/(1 - arctanh(2*x))^(1/2).

1, 1, 3, 23, 201, 2529, 36027, 633975, 12445521, 282376065, 7045758003, 196111046295, 5929900611225, 195773173735905, 6950809317622635, 265652001656970615, 10828342476187312545, 470368564694268015105, 21643209863062015977315, 1053344875062427351601175

Offset: 0

Author

Seiichi Manyama, Jun 30 2025

Keywords

• nonn
• easy

Crossrefs

Cf. A296676, A385473.

Cf. A001147, A111594.

Programs

PARI

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

Formula

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

a(n) = Sum_{k=0..n} A001147(k) * 2^(n-k) * A111594(n,k).