A381447 E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^2 * cosh(x*A(x)^2).

1, 1, 4, 33, 432, 7745, 175680, 4818457, 155138816, 5738752161, 239890406400, 11184338164241, 575437530083328, 32387311520034913, 1979498673768132608, 130566701113312750665, 9244392468538216611840, 699309477932976288024257, 56289911059840766752456704

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• nonn

Comments

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

Links

• Index entries for reversions of series

Crossrefs

Cf. A381171, A381448.

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

Formula

E.g.f.: ( (1/x) * Series_Reversion( x/(1 + x * cosh(x))^2 ) )^(1/2).

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