A382826 a(n) = Sum_{k=0..n} (k! * Stirling1(n+1,k+1))^2.

1, 2, 17, 337, 12152, 696076, 58136500, 6673107316, 1008077743552, 193915431216576, 46281189562936704, 13420575661095930240, 4647502230640182602496, 1894412230202331489632256, 897850527136410029486517504, 489578762044356075253626875136

Offset: 0

Author

Seiichi Manyama, Apr 06 2025

Keywords

• nonn

Crossrefs

Main diagonal of A382823.

Cf. A048163, A382792.

Programs

PARI

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

Formula

a(n) = (n!)^2 * [(x*y)^n] 1 / ( (1-x) * (1-y) * (1 - log(1-x) * log(1-y)) ).

a(n) = (n!)^2 * [(x*y)^n] 1 / ( (1+x) * (1+y) * (1 - log(1+x) * log(1+y)) ).