A380719 E.g.f. A(x) satisfies A(x) = exp(x / (1 - x*A(x))^2) / (1 - x*A(x)).

1, 2, 13, 157, 2817, 67541, 2033293, 73793399, 3137724033, 153046171657, 8425546124661, 516854537135795, 34963627698674689, 2585888583437930525, 207593192181190597629, 17978635157682679541311, 1670861912137958623651329, 165868047783912942721097873, 17517226956387964424430057829

Offset

0,2

Links

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

Formula

a(n) = n! * Sum_{k=0..n} (n-k+1)^(k-1) * binomial(2*n,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (n-k+1)^(k-1)*binomial(2*n, n-k)/k!);

Crossrefs

Cf. A380663, A380718.

Sequence in context: A366012 A297408 A377571 * A316701 A379575 A062593

Adjacent sequences: A380716 A380717 A380718 * A380720 A380721 A380722

Keyword

nonn,new

Author

Seiichi Manyama, Jan 30 2025

Status

approved