A377550 E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x*A(x)^4).

1, 1, 4, 45, 772, 17865, 525966, 18794881, 790175128, 38221092657, 2091074167450, 127675964340441, 8606833626646740, 634928943628432921, 50878715440232312374, 4400937219238706030865, 408700742920092110904496, 40558224679468186878237153, 4283310197644529184427059378

Offset: 0

Author

Seiichi Manyama, Oct 31 2024

Keywords

• nonn

Crossrefs

Cf. A161633, A364980, A364981.

Cf. A377551, A377552.

Programs

PARI

a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*n-3*k+1, k)/((4*n-3*k+1)*(n-k)!));

Formula

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(4*n-3*k+1,k)/( (4*n-3*k+1)*(n-k)! ).