A349965 a(n) = Sum_{k=0..n} (k * (n-k))^k.

1, 1, 2, 7, 47, 513, 8020, 169227, 4637965, 159568981, 6684686230, 332681461871, 19316990453131, 1292074091000105, 98636639620170792, 8528989125071254867, 829516920337723299465, 90124512307642049807293, 10865612430780251465538154

Offset: 0

Author

Seiichi Manyama, Dec 07 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..286

Crossrefs

Cf. A026898, A100262, A349966.

Programs

Mathematica

a[n_] := Sum[If[k == 0, 1, (k*(n - k))^k], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Dec 07 2021 *)

PARI

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

Formula

log(a(n)) ~ n*(2*log(n) - 1 + (1/(2*log(n)) - 1)*log(2*log(n))). - Vaclav Kotesovec, Dec 07 2021