A381408 E.g.f. A(x) satisfies A(x) = exp( 2 * x * cosh(x * A(x)) ).

1, 2, 4, 14, 160, 2202, 28384, 419302, 8238080, 193340978, 4860711424, 132391420350, 4045976651776, 137295166640842, 5028417873133568, 197042617602645398, 8292209178735935488, 374117497443421923426, 17958577129581151387648, 912189896002576287703918

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• nonn

Comments

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

Crossrefs

Cf. A185951, A381407.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = 2*sum(k=0, n, (2*n-2*k+2)^(k-1)*a185951(n, k));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381407.

a(n) = 2 * Sum_{k=0..n} (2*n-2*k+2)^(k-1) * A185951(n,k).