A371228 E.g.f. satisfies A(x) = 1 - x*A(x)*log(1 - x*A(x)^2).

1, 0, 2, 3, 80, 510, 12084, 164640, 4272736, 91935648, 2769703920, 80692896240, 2849745645504, 103479044628960, 4250475820200960, 183436357950387360, 8649275730513361920, 430735131434242736640, 22999938416454315239424, 1295673669960473064844800

Offset: 0

Author

Seiichi Manyama, Mar 15 2024

Keywords

• nonn

Crossrefs

Cf. A371227, A371229, A371230.

Cf. A371121.

Programs

PARI

a(n) = n!*sum(k=0, n\2, (2*n-k)!*abs(stirling(n-k, k, 1))/((n-k)!*(2*n-2*k+1)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (2*n-k)! * |Stirling1(n-k,k)|/( (n-k)! * (2*n-2*k+1)! ).