A356673 a(n) = n! * Sum_{k=0..n} k^(3*(n-k))/k!.

1, 1, 3, 31, 901, 45741, 3960871, 584698843, 130554106761, 40790044059481, 17681098707667531, 10491554658622447191, 8198225417359164798733, 8172446419302496167191941, 10264848632098736708582150511

Offset: 0

Author

Seiichi Manyama, Aug 22 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..185

Crossrefs

Cf. A354436, A356672.

Cf. A349880, A356629, A358687.

Programs

PARI

a(n) = n!*sum(k=0, n, k^(3*(n-k))/k!);

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k^3*x)))))

Formula

E.g.f: Sum_{k>=0} x^k / (k! * (1 - k^3 * x)).