A377552 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)^2))^2.

1, 2, 10, 114, 2000, 47050, 1399452, 50386406, 2130643216, 103530094866, 5684985037460, 348165567064942, 23530146364469208, 1739586913373486138, 139658209205202262876, 12099843726478251739830, 1125274333255817053205792, 111809642081518362872011042, 11821367007844973309548419876

Offset: 0

Author

Seiichi Manyama, Oct 31 2024

Keywords

• nonn

Crossrefs

Cf. A377550, A377551.

Programs

PARI

a(n) = 2*n!*sum(k=0, n, k^(n-k)*binomial(4*n-3*k+2, k)/((4*n-3*k+2)*(n-k)!));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377550.

a(n) = 2 * n! * Sum_{k=0..n} k^(n-k) * binomial(4*n-3*k+2,k)/( (4*n-3*k+2)*(n-k)! ).