A349886 a(n) = Sum_{k=0..n} k^(k*n).

1, 2, 18, 19749, 4295498995, 298024323402930834, 10314425729813391637014599924, 256923578002288684397369021397408936103993, 6277101735598268377660667072561845282166297358613176925573

Offset: 0

Author

Seiichi Manyama, Dec 03 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..26

Crossrefs

Cf. A031971, A062970, A249459.

Programs

Mathematica

Table[1 + Sum[k^(k*n), {k, 1, n}], {n, 0, 10}] (* Vaclav Kotesovec, Dec 04 2021 *)
a[n_] := Sum[If[k == 0, 1, k^(k*n)], {k, 0, n}]; Array[a, 9, 0] (* Amiram Eldar, Dec 04 2021 *)

PARI

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

PARI

my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, k^k^2*x^k/(1-k^k*x)))

Formula

G.f.: Sum_{k>=0} k^(k^2) * x^k/(1 - k^k * x).

a(n) ~ n^(n^2). - Vaclav Kotesovec, Dec 04 2021