A382828 a(n) = Sum_{k=0..n} (k!)^2 * binomial(k+2,2) * Stirling1(n+1,k+1)^2.

1, 4, 55, 1623, 82116, 6302028, 680105112, 98011315608, 18163969766592, 4205977241171328, 1189459906531372224, 403300593144673493184, 161454763431242385682176, 75337361633768810384542464, 40524573487904551618353921024, 24890567631479746511661428751360

Offset: 0

Author

Seiichi Manyama, Apr 06 2025

Keywords

• nonn

Crossrefs

Main diagonal of A382825.

Cf. A382676, A382806.

Programs

PARI

a(n) = sum(k=0, n, k!^2*binomial(k+2, 2)*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))^3 ).

a(n) = (n!)^2 * [(x*y)^n] 1 / ( (1+x) * (1+y) * (1 - log(1+x) * log(1+y))^3 ).