A371270 E.g.f. satisfies A(x) = 1 + x*A(x)^2 * (exp(x*A(x)^2) - 1).

1, 0, 2, 3, 100, 605, 18366, 238147, 7688584, 162016857, 5839673410, 172051422191, 7034104918380, 265080848463301, 12311587474831750, 561485310426413115, 29475848282815342096, 1569372890780660724401, 92402629467727290784650

Offset: 0

Author

Seiichi Manyama, Mar 16 2024

Keywords

• nonn

Crossrefs

Cf. A371262, A371269, A371271.

Cf. A371229.

Programs

PARI

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

Formula

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