A381446 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x) * A(x)^3 ).

1, 1, 8, 135, 3456, 120245, 5303040, 283559227, 17830210048, 1289406976713, 105435719470080, 9619902621234191, 968905466782150656, 106779534666615500989, 12781543241568143171584, 1651368425166943566943875, 229049483642619517308764160, 33947359023461155854768564497

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• nonn

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Crossrefs

Cf. A205571, A295256, A381445.

Cf. A185951.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(4*k+1, k)/(4*k+1)*a185951(n, k));

Formula

a(n) = Sum_{k=0..n} k! * binomial(4*k+1,k)/(4*k+1) * A185951(n,k).