A382678 a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+3,3) * Stirling2(n+1,k+1)^2.

1, 5, 77, 2357, 118061, 8712245, 886143917, 118592620277, 20176999414061, 4249819031692085, 1084956766012858157, 329975948760472311797, 117851658189070970988461, 48830366210401091606537525, 23228207308210113849419226797, 12571433948267218576823401692917

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = (n!)^2 * [(x*y)^n] exp(x+y) / (exp(x) + exp(y) - exp(x+y))^4.

Prog

(PARI) a(n) = sum(k=0, n, k!^2*binomial(k+3, 3)*stirling(n+1, k+1, 2)^2);

Crossrefs

Main diagonal of A382674.

Cf. A048163, A092552, A382676.

Sequence in context: A287041 A360351 A318236 * A009485 A188455 A015056

Adjacent sequences: A382675 A382676 A382677 * A382679 A382680 A382681

Keyword

nonn

Author

Seiichi Manyama, Apr 03 2025

Status

approved