A381407 E.g.f. A(x) satisfies A(x) = exp( x * cosh(x * A(x)^2) ).

1, 1, 1, 4, 61, 756, 8581, 125168, 2577849, 60269968, 1469636041, 39496750272, 1212192326005, 41147125079360, 1496063100479949, 58263746530145536, 2447130544401729649, 110270888250759852288, 5279535712822539622033, 267412182631190346232832

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, A381376.

Programs

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, (2*n-2*k+1)^(k-1)*a185951(n, k));

Formula

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