A382827 a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n+1,k+1)^2.

1, 3, 34, 854, 37556, 2546852, 246113904, 32104625520, 5433891955968, 1157778241057152, 303197684900579712, 95717977509042032256, 35847800701044816248064, 15713483696924130220098816, 7969364997624587289470810112, 4630203661005094483980386924544

Offset: 0

Author

Seiichi Manyama, Apr 06 2025

Keywords

• nonn

Crossrefs

Main diagonal of A382824.

Cf. A092552, A382804.

Programs

PARI

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

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