A360935 Expansion of e.g.f. Sum_{k>=0} exp((k^k - 1)*x) * x^k/k!.

1, 1, 1, 10, 159, 8306, 1346855, 801620870, 2064941077199, 20691706495244482, 1137052204448926181679, 255128692791512749880418782, 348784909594653094321340422905383, 2262992285674206001784964011734257207938

Offset: 0

Author

Seiichi Manyama, Feb 26 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A001831, A360933, A360934.

Cf. A355464.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1+x+sum(k=2, N, exp((k^k-1)*x)*x^k/k!)))

PARI

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

PARI

a(n) = sum(k=0, n, (k^k-1)^(n-k)*binomial(n, k));

Formula

G.f.: Sum_{k>=0} x^k/(1 - (k^k - 1)*x)^(k+1).

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