A380919 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-3*x/(1 - x)) ).

1, 4, 55, 1380, 51213, 2533968, 157230099, 11752365600, 1028673637785, 103250018926080, 11693974366638639, 1475530063767972864, 205281631888995454245, 31221155498006896773120, 5153702313885813394180875, 917695970480270443222536192, 175344823710094148613399084849

Offset

0,2

Links

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

Index entries for reversions of series

Formula

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

a(n) = n! * Sum_{k=0..n} 3^k * (n+1)^(k-1) * binomial(2*n,n-k)/k!.

Prog

(PARI) a(n, q=3, r=3, s=3, t=1, u=1/3) = 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. A380663, A380918.

Cf. A380917.

Sequence in context: A195634 A322627 A206384 * A379662 A271715 A099122

Adjacent sequences: A380916 A380917 A380918 * A380921 A380929 A380930

Keyword

nonn,new

Author

Seiichi Manyama, Feb 08 2025

Status

approved