A371146 E.g.f. satisfies A(x) = 1/(1 - x*A(x)^2)^(x*A(x)^2).

1, 0, 2, 3, 116, 690, 24714, 315840, 11919088, 250812072, 10389272040, 310700914920, 14351129171400, 557402214180240, 28831564284582864, 1372162923004025880, 79345973798740154880, 4450055092134985771200, 286324089075857021558976

Offset: 0

Author

Seiichi Manyama, Mar 13 2024

Keywords

• nonn

Crossrefs

Cf. A184949, A356786, A356795.

Cf. A371023.

Programs

PARI

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

Formula

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