A371043 E.g.f. satisfies A(x) = 1 + x^2*A(x)*exp(x*A(x)).

1, 0, 2, 6, 36, 380, 3630, 47082, 725816, 12132360, 235801530, 5083309550, 119757623172, 3103443520476, 87082536196838, 2632399338834930, 85471932351187440, 2961803643600574352, 109154615479427298546, 4264407640037365789014, 175984871341042826680700

Offset: 0

Author

Seiichi Manyama, Mar 09 2024

Keywords

• nonn

Crossrefs

Cf. A370984, A371018, A371042.

Cf. A365282.

Programs

PARI

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

Formula

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