A381986 E.g.f. A(x) satisfies A(x) = exp(x) * B(x*A(x)^2), where B(x) = 1 + x*B(x)^3 is the g.f. of A001764.

1, 2, 17, 388, 14329, 727206, 46984729, 3689119624, 341097752657, 36302764864330, 4371463743828481, 587606216836328460, 87219196719691250185, 14168990447072685567214, 2500554381188629649979593, 476391652257266128440376336, 97447147561230881896398507553

Offset: 0

Author

Seiichi Manyama, Mar 11 2025

Keywords

• nonn

Crossrefs

Cf. A381984, A381985.

Cf. A001764, A002294, A382000.

Programs

PARI

a(n) = n!*sum(k=0, n, (2*k+1)^(n-k)*binomial(5*k+1, k)/((5*k+1)*(n-k)!));

Formula

Let F(x) be the e.g.f. of A382000. F(x) = B(x*A(x)^2) = exp( 1/3 * Sum_{k>=1} binomial(3*k,k) * (x*A(x)^2)^k/k ).

a(n) = n! * Sum_{k=0..n} (2*k+1)^(n-k) * A002294(k)/(n-k)!.