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

0,3

Links

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

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).

a(n) ~ 2^(n + 3/2) * (exp(2) + 1)^(n - 1/2) * n^n / (exp(n-1) * (exp(2) - 1)^(n + 1/2)). - Vaclav Kotesovec, Sep 30 2025

Prog

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

Crossrefs

Cf. A296676, A385473.

Cf. A001147, A111594.

Sequence in context: A096649 A370283 A235131 * A235360 A135423 A114017

Adjacent sequences: A385469 A385470 A385471 * A385473 A385474 A385475

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 30 2025

Status

approved