A377579 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)))^4.

1, 4, 20, 204, 3112, 61220, 1523064, 45456292, 1586426720, 63461164932, 2862300600040, 143766016251044, 7959047336014416, 481550056915454020, 31615435540393172888, 2238661916541220434660, 170070509857455107126464, 13798559748847266924993284, 1190848786811966457102586824

Offset: 0

Author

Seiichi Manyama, Nov 02 2024

Keywords

• nonn

Crossrefs

Cf. A161632, A377578.

Cf. A377580, A377581.

Programs

PARI

a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*n-4*k+4, k)/((n-k+1)*(n-k)!));

Formula

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377581.

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(4*n-4*k+4,k)/( (n-k+1)*(n-k)! ).