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%I #18 Dec 28 2023 09:22:02
%S 1,1,6,48,516,6955,112686,2132634,46167560,1125116901,30481672610,
%T 908760877244,29565986232396,1042354163621927,39584173937284438,
%U 1610922147768721590,69940319175066857488,3226793787576474492657,157649292247463953189578
%N a(n) = Sum_{k=0..n} n^k * k^(n-k).
%H Seiichi Manyama, <a href="/A351340/b351340.txt">Table of n, a(n) for n = 0..386</a>
%F a(n) = [x^n] Sum_{k>=0} (n*x)^k/(1 - k*x).
%F a(n) ~ c * n^(n + 1/2), where c = sqrt(Pi)/2. - _Vaclav Kotesovec_, Feb 09 2022
%t a[0] = 1; a[n_] := Sum[n^k * k^(n - k), {k, 0, n}]; Array[a, 20, 0] (* _Amiram Eldar_, Feb 08 2022 *)
%o (PARI) a(n) = sum(k=0, n, n^k*k^(n-k));
%Y Main diagonal of A351339.
%Y Cf. A026898, A031973, A155956, A303991.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Feb 08 2022
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