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%I #18 Dec 08 2021 06:49:03
%S 1,1,3,16,141,1871,34951,873174,27951929,1107415549,52891809491,
%T 2987861887924,196828568831365,14950745148070499,1296606974501951743,
%U 127238563043551898986,14012626653816435643633,1719136634276882827095009,233448782800118609096218891
%N a(n) = Sum_{k=0..n} (k*n)^(n-k).
%H Seiichi Manyama, <a href="/A349969/b349969.txt">Table of n, a(n) for n = 0..284</a>
%F a(n) = [x^n] Sum_{k>=0} x^k/(1 - n*k * x).
%F a(n) ~ sqrt(2*Pi/(n*(1 + LambertW(exp(1)*n^2)))) * (n^2/LambertW(exp(1)*n^2))^(n + 1/2 - n/LambertW(exp(1)*n^2)). - _Vaclav Kotesovec_, Dec 07 2021
%t a[n_] := Sum[If[k == n == 0, 1, (k*n)^(n - k)], {k, 0, n}]; Array[a, 19, 0] (* _Amiram Eldar_, Dec 07 2021 *)
%o (PARI) a(n) = sum(k=0, n, (k*n)^(n-k));
%Y Cf. A026898, A155956, A349964, A349970.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Dec 07 2021
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