A381450 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x * cosh(x))^3 ).

1, 3, 24, 339, 7056, 195855, 6819840, 286105071, 14055420288, 791783681499, 50327779368960, 3563709848656683, 278223968271034368, 23744747385054558759, 2199369837961901789184, 219748696455778150645575, 23559108001707680103628800, 2697737574531326391439989171

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..17.

Index entries for reversions of series

Formula

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A381448.

a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(3*n+3,k) * 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(3*n+3, k)*a185951(n, k))/(n+1);

Crossrefs

Cf. A381171, A381449.

Cf. A377554, A381443.

Cf. A185951, A381448.

Sequence in context: A381443 A380808 A371007 * A144003 A334775 A153389

Adjacent sequences: A381447 A381448 A381449 * A381461

Keyword

nonn,new

Author

Seiichi Manyama, Feb 23 2025

Status

approved