A380724 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^3) / (1 - x*A(x)^3).

1, 2, 29, 862, 39461, 2454296, 193406953, 18475039808, 2075062993865, 268013104242688, 39139481641977461, 6377306725457207552, 1147019426037344539501, 225728971809041691392000, 48248339461852786811399489, 11131014193619108036340637696, 2756799306857952163745291500433

Offset: 0

Author

Seiichi Manyama, Jan 30 2025

Keywords

• nonn

Crossrefs

Cf. A377831, A380723.

Cf. A373324, A377889.

Cf. A360609.

Programs

PARI

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

Formula

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