A341331 a(n) = n^n - (n-1)^n - (n-2)^n - ... - 1^n.

1, 3, 18, 158, 1825, 26141, 446782, 8869820, 200535993, 5085658075, 142947350986, 4410243535402, 148156328308105, 5382924338773177, 210309307208574750, 8791961076113491704, 391581231268402937041, 18510377905675629883959, 925555262359725659407258

Offset: 1

Author

Seiichi Manyama, Feb 09 2021

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..386

Crossrefs

Cf. A000312, A031971, A080956, A121706, A179297, A179298, A173142, A191686, A290844.

Programs

Maple

f:= proc(n) local k;  n^n - add(k^n,k=1..n-1) end proc:
map(f, [$1..30]); # Robert Israel, Feb 10 2021

Mathematica

a[n_] := n^n - Sum[k^n, {k, 0, n - 1}]; Array[a, 20] (* Amiram Eldar, Apr 28 2021 *)

PARI

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

Formula

a(n) = A000312(n) - A121706(n).

a(n) = - A290844(n-1,n) for n > 1.