A381442 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + sinh(x))^2 ).

1, 2, 10, 86, 1080, 18042, 377936, 9538622, 281946496, 9557102450, 365548361472, 15576454300134, 731807446707200, 37584596599753322, 2094995668172597248, 125966553940498047182, 8127048592610380578816, 560040497770823162810082, 41054563701320694564061184

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A136630, A198865.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(2*n+2, k)*a136630(n, k))/(n+1);

Formula

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A198865.

a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(2*n+2,k) * A136630(n,k).