A377551 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)))^4.

1, 4, 28, 348, 6424, 156900, 4788024, 175678468, 7538078944, 370557062532, 20540717542120, 1267858489975044, 86252943572785488, 6412719306748404676, 517341051818833834648, 45012757582472804739780, 4201834386001491870902464, 418891045572216881436564228

Offset: 0

Author

Seiichi Manyama, Oct 31 2024

Keywords

• nonn

Crossrefs

Cf. A161633, A377541, A377545.

Cf. A377550, A377552.

Programs

PARI

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

Formula

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377550.

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