A382034 E.g.f. A(x) satisfies A(x) = exp(x*B(x*A(x))^4), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.

1, 1, 9, 181, 5713, 246881, 13570081, 906180997, 71250724833, 6448375469665, 660286026034561, 75472025139452261, 9525947428687403473, 1315935073971181422721, 197485196722573989608289, 31993978774204625549549221, 5565216938342017912128576961, 1034506012356981473110554574145

Offset: 0

Author

Seiichi Manyama, Mar 12 2025

Keywords

• nonn

Crossrefs

Cf. A161630, A382032, A382033.

Cf. A002293, A377630.

Programs

PARI

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

Formula

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

Let F(x) be the e.g.f. of A377630. F(x) = log(A(x))/x = B(x*A(x))^4.

E.g.f.: A(x) = exp( Series_Reversion( x/(1 + x*exp(x))^4 ) ).