A382804 a(n) = Sum_{k=0..n} k! * (k+1)! * Stirling1(n,k)^2.

1, 2, 14, 260, 9588, 581952, 52096512, 6423520896, 1041005447424, 214260350714496, 54547409318781312, 16820040059243046144, 6175245603727007034624, 2661063379044058584861696, 1329787781176741647226481664, 762665713456216694195942866944

Offset

0,2

Links

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

Formula

a(n) == 0 (mod 2) for n > 0.

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

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

a(n) ~ sqrt(Pi) * n^(2*n + 3/2) / (exp(1) - 1)^(2*n+2). - Vaclav Kotesovec, Apr 05 2025

Prog

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

Crossrefs

Main diagonal of A382799.

Cf. A382792, A382806.

Cf. A382737.

Sequence in context: A070813 A156214 A370490 * A187654 A280517 A373222

Adjacent sequences: A382801 A382802 A382803 * A382805 A382806 A382807

Keyword

nonn

Author

Seiichi Manyama, Apr 05 2025

Status

approved