A381416 E.g.f. A(x) satisfies A(x) = exp( 2 * sinh(x * A(x)) ).

1, 2, 12, 130, 2080, 44354, 1185856, 38188546, 1439993088, 62261776002, 3037542875136, 165090563653250, 9892965209886720, 648064548551770562, 46075919968420085760, 3533725068594022938626, 290804441398399410503680, 25561250854199444302177538, 2390133356713125694150017024

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• nonn

Crossrefs

Cf. A136630, A381415.

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) = 2*sum(k=0, n, (2*n+2)^(k-1)*a136630(n, k));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381415.

a(n) = 2 * Sum_{k=0..n} (2*n+2)^(k-1) * A136630(n,k).