A381376 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x * A(x)^2) ).

1, 1, 2, 9, 96, 1385, 22080, 403417, 8829184, 227956689, 6667822080, 215780258441, 7674505073664, 298885308910201, 12661212551163904, 578940699178779225, 28400662193828659200, 1488075298726340008097, 82965096417136263561216, 4904558063539270185865609

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} k! * binomial(2*n-k+1,k)/(2*n-k+1) * A185951(n,k).

Prog

(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(2*n-k+1, k)/(2*n-k+1)*a185951(n, k));

Crossrefs

Cf. A381171, A381300.

Cf. A185951, A381377.

Sequence in context: A086992 A354316 A345466 * A115965 A001142 A111847

Adjacent sequences: A381371 A381373 A381374 * A381377 A381378 A381379

Keyword

nonn,new

Author

Seiichi Manyama, Feb 22 2025

Status

approved