A380754 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2 / (1 - x * A(x)^2)) / (1 - x * A(x)^2)^2.

1, 3, 49, 1585, 78093, 5201771, 437861149, 44607800385, 5338028587705, 734060947570867, 114078994869344841, 19773620424489710417, 3782330144139700656325, 791450463143064447635355, 179843077195936890250320373, 44102411207136266014669068961, 11609166496582801689148704120561

Offset: 0

Author

Seiichi Manyama, Feb 01 2025

Keywords

• nonn

Crossrefs

Cf. A380726.

Programs

PARI

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

Formula

a(n) = n! * Sum_{k=0..n} (2*n+1)^(k-1) * binomial(5*n+1,n-k)/k!.