A380717 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2 * (1 - x*A(x))^2) / (1 - x*A(x)).

1, 2, 13, 151, 2561, 57401, 1602985, 53659453, 2095244289, 93523526065, 4698386208521, 262397580544133, 16128832249562785, 1082120615743840297, 78695060375718726633, 6166431270471329586301, 517970728078392717716225, 46432097598077316120950369, 4424506354750061857673476873

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-2*k,n-k)/k!.

Prog

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

Crossrefs

Cf. A194471, A380673.

Sequence in context: A069736 A363846 A058192 * A379456 A367820 A377831

Adjacent sequences: A380711 A380712 A380716 * A380718 A380719 A380720

Keyword

nonn

Author

Seiichi Manyama, Jan 30 2025

Status

approved