A371262 E.g.f. satisfies A(x) = 1 + x * (exp(x*A(x)^2) - 1).

1, 0, 2, 3, 52, 365, 5286, 76867, 1341320, 27823833, 624467530, 16163482511, 452003629452, 13975370745349, 467133121195118, 16865722845267675, 653859200911607056, 27061461284541490097, 1192488605596282310802, 55686113074253206544167

Offset: 0

Author

Seiichi Manyama, Mar 16 2024

Keywords

• nonn

Crossrefs

Cf. A371269, A371270, A371271.

Cf. A371227.

Programs

PARI

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

Formula

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