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Numerator of n^(n-1)/n!.
4

%I #26 Sep 08 2022 08:44:52

%S 1,1,3,8,125,54,16807,16384,531441,156250,2357947691,2985984,

%T 1792160394037,7909306972,320361328125,35184372088832,

%U 2862423051509815793,5083731656658,5480386857784802185939,32000000000000000,41209797661291758429

%N Numerator of n^(n-1)/n!.

%C (-1)^(n+1)* n-th numerator of coefficient in LambertW(x) power series, where LambertW(x) is the transcendental function satisfying LambertW(x)*exp( LambertW(x) )=x. - _Benoit Cloitre_, May 08 2002

%H G. C. Greubel, <a href="/A036504/b036504.txt">Table of n, a(n) for n = 1..250</a>

%t Numerator[Table[n^(n - 1)/n!, {n, 1, 30}]] (* _G. C. Greubel_, Sep 09 2018 *)

%t CoefficientList[-LambertW[-x]/x + O[x]^21, x] // Numerator (* _Jean-François Alcover_, Jan 15 2019 *)

%o (PARI) for(n=1, 30, print1(numerator(n^(n-1)/n!), ", ")) \\ _G. C. Greubel_, Sep 09 2018

%o (Magma) [Numerator(n^(n-1)/Factorial(n)): n in [1..30]]; // _G. C. Greubel_, Sep 09 2018

%o (Sage) [numerator(n^(n-1)/factorial(n)) for n in (1..30)] # _G. C. Greubel_, Feb 08 2019

%Y Cf. A036503 (denominators).

%Y A095996 is a better version of the denominators of the LambertW function. - _N. J. A. Sloane_, Jan 08 2021

%K nonn,frac

%O 1,3

%A _N. J. A. Sloane_