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%I #24 Sep 08 2022 08:45:00
%S 1,3,15,109,1061,13081,196135,3470097,70807497,1637267473,42310099331,
%T 1208419463329,37799118682429,1285103316125721,47184372451150719,
%U 1860687091374107761,78432185337652592657,3519258710478790607137,167474007086529472461307
%N a(n) = (n-1)! * Sum_{k=1..n} k^k/k!.
%H G. C. Greubel, <a href="/A054201/b054201.txt">Table of n, a(n) for n = 1..385</a>
%F -LambertW(-x)/(1+LambertW(-x))/(1-x) = Sum_{n>=1} a(n)*x^n/(n-1)!. - _Vladeta Jovovic_, Aug 26 2002
%F a(n) ~ exp(1)/(exp(1)-1) * n^(n-1). - _Vaclav Kotesovec_, Oct 18 2013
%F a(n) = (n-1)!*Sum_{i=1..n} Product_{j=1..i} i/j. - _Pedro Caceres_, Apr 19 2019
%e a(3) = 2! *(1^1/1! + 2^2/2! + 3^3/3!) = 2 *(1/1 + 4/2 + 27/6) = 15.
%t Table[(n-1)!*Sum[k^k/k!,{k,1,n}],{n,1,20}] (* _Vaclav Kotesovec_, Oct 18 2013 *)
%o (PARI) vector(20, n, (n-1)!*sum(k=1,n, k^k/k!)) \\ _G. C. Greubel_, Jul 31 2019
%o (Magma) F:=Factorial; [F(n-1)*(&+[k^k/F(k): k in [1..n]]): n in [1..20]]; // _G. C. Greubel_, Jul 31 2019
%o (Sage) f=factorial; [f(n-1)*sum(k^k/f(k) for k in (1..n)) for n in (1..20)] # _G. C. Greubel_, Jul 31 2019
%o (GAP) F:=Factorial;; List([1..20], n-> F(n-1)*Sum([1..n], k-> k^k/F(k))); # _G. C. Greubel_, Jul 31 2019
%Y Cf. A054202.
%K nonn,easy
%O 1,2
%A _Leroy Quet_, Apr 29 2000
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