A380915 - OEIS

A380915

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

1, 2, 19, 421, 14453, 676741, 40225525, 2901397997, 246222420841, 24038780973913, 2654362957336481, 327087730518759937, 44498835149618922253, 6624743172003104909957, 1071295799491745519081629, 186999332904147675923216341, 35044146207707289182759039825

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

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

PROG

(PARI) a(n, q=1, r=3, s=0, t=1, u=1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);

CROSSREFS

Cf. A380769, A380914.

Cf. A380727.