A349964 - OEIS

%I #21 Dec 07 2021 10:59:31

%S 1,1,20,972,90624,13828125,3133930176,988501957072,414139067400192,

%T 222497518123837665,149143419250000000000,122020951254446884154196,

%U 119671520043865789861724160,138593796657903100873209121453

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

%F a(n) = n^n * [x^n] Sum_{k>=0} (k * x)^k/(1 - k * x) = n^n * A031971(n).

%F a(n) ~ c * n^(2*n), where c = 1/(1 - 1/exp(1)) = A185393. - _Vaclav Kotesovec_, Dec 07 2021

%t a[n_] := Sum[If[k == n == 0, 1, (k*n)^n], {k, 0, n}]; Array[a, 14, 0] (* _Amiram Eldar_, Dec 07 2021 *)

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

%Y Cf. A031971, A155956, A185393, A349966, A349969,

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 07 2021