%I #16 Dec 08 2021 06:49:55
%S 1,1,2,7,47,513,8020,169227,4637965,159568981,6684686230,332681461871,
%T 19316990453131,1292074091000105,98636639620170792,
%U 8528989125071254867,829516920337723299465,90124512307642049807293,10865612430780251465538154
%N a(n) = Sum_{k=0..n} (k * (n-k))^k.
%H Seiichi Manyama, <a href="/A349965/b349965.txt">Table of n, a(n) for n = 0..286</a>
%F log(a(n)) ~ n*(2*log(n) - 1 + (1/(2*log(n)) - 1)*log(2*log(n))). - _Vaclav Kotesovec_, Dec 07 2021
%t a[n_] := Sum[If[k == 0, 1, (k*(n - k))^k], {k, 0, n}]; Array[a, 19, 0] (* _Amiram Eldar_, Dec 07 2021 *)
%o (PARI) a(n) = sum(k=0, n, (k*(n-k))^k);
%Y Cf. A026898, A100262, A349966.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Dec 07 2021