A381140 Expansion of e.g.f. exp( -LambertW(-x * cosh(x)) ).

1, 1, 3, 19, 161, 1781, 24667, 409991, 7959233, 176920489, 4432942931, 123648692795, 3800647961761, 127654261471517, 4651982506605995, 182824074836850991, 7708128977570816129, 347059689259637711441, 16621016953663100702755, 843658152872351669816675

Offset: 0

Author

Seiichi Manyama, Feb 15 2025

Keywords

• nonn

Comments

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

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A003727, A162649, A381143.

Cf. A185951.

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

Formula

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

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