A381377 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x * A(x)) )^2.

1, 2, 6, 30, 288, 4090, 68160, 1292774, 28627200, 739821618, 21729070080, 708442911022, 25365382259712, 992297344710698, 42173572623716352, 1934344590577340790, 95175474351245230080, 5000227637170108004194, 279428527333796676894720, 16552583621200571079876158

Offset: 0

Author

Seiichi Manyama, Feb 22 2025

Keywords

• nonn

Comments

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

Crossrefs

Cf. A185951, A381206, A381376.

Programs

PARI

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381376.

a(n) = 2 * Sum_{k=0..n} k! * binomial(2*n-k+2,k)/(2*n-k+2) * A185951(n,k).