A381448 E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^3 * cosh(x*A(x)^3).

1, 1, 6, 75, 1464, 39065, 1324080, 54460987, 2635269504, 146681897553, 9233067686400, 648538095601451, 50289434320131072, 4267083467872455529, 393266542856236148736, 39121731305087283953115, 4178124995723585643970560, 476806534212831941528989217, 57905078072597558361906610176

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, A381447.

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(3*n+1, k)*a185951(n, k))/(3*n+1);

Formula

E.g.f.: ( (1/x) * Series_Reversion( x/(1 + x * cosh(x))^3 ) )^(1/3).

a(n) = (1/(3*n+1)) * Sum_{k=0..n} k! * binomial(3*n+1,k) * A185951(n,k).