A356883 E.g.f. satisfies: A(x)^2 * log(A(x)) = x * (exp(x*A(x)) - 1).

1, 0, 2, 3, -8, 5, 696, 2527, -40144, -178407, 8337880, 76134971, -1781542344, -24938260763, 691630553264, 14216543752335, -312910463346464, -9343318015483471, 195539694928047144, 8145971436703039363, -142317653823753257560, -8498984155838272275459

Offset: 0

Author

Seiichi Manyama, Sep 02 2022

Keywords

• sign

Crossrefs

Cf. A349560, A356785, A356788, A356789, A356882.

Cf. A355763.

Programs

PARI

a(n) = n!*sum(k=0, n\2, (n-3*k+1)^(k-1)*stirling(n-k, k, 2)/(n-k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-3*k+1)^(k-1) * Stirling2(n-k,k)/(n-k)!.