%I #12 Sep 08 2022 08:45:00

%S 1,3,14,102,1032,12840,194400,3457440,70680960,1635863040,42293664000,

%T 1208201702400,37796100249600,1285064055475200,47183768081049600,

%U 1860676781483520000,78432007085752320000,3519255355814854656000

%N a(n) = (n-1)! * Sum_{k=1..n} floor(k^k/k!).

%H G. C. Greubel, <a href="/A054202/b054202.txt">Table of n, a(n) for n = 1..380</a>

%t Table[(n-1)!*Sum[Floor[k^k/k!], {k, n}], {n, 20}] (* _G. C. Greubel_, Jul 31 2019 *)

%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)*(&+[Floor(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(floor(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-> Int(k^k/F(k)) )); # _G. C. Greubel_, Jul 31 2019

%Y Cf. A054201.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Apr 29 2000