A381449 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x * cosh(x))^2 ).

1, 2, 10, 90, 1224, 22450, 517920, 14395514, 468414464, 17474840226, 735559614720, 34491849224602, 1783268816102400, 100786369113730898, 6182264844496971776, 409065938149354422330, 29043282491002728284160, 2202461172795524123296834, 177675452451923238962528256

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..18.

Index entries for reversions of series

Formula

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381447.

a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(2*n+2,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(2*n+2, k)*a185951(n, k))/(n+1);

Crossrefs

Cf. A381171, A381450.

Cf. A185951, A381447.

Sequence in context: A326089 A377541 A277403 * A179423 A320962 A067550

Adjacent sequences: A381446 A381447 A381448 * A381450 A381461 A381467

Keyword

nonn,new

Author

Seiichi Manyama, Feb 23 2025

Status

approved