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%I #17 Sep 08 2022 08:44:52
%S 1,2,2,3,24,5,720,315,4480,567,3628800,1925,479001600,868725,14350336,
%T 638512875,20922789888000,14889875,6402373705728000,14849255421,
%U 7567605760000,17717861581875,1124000727777607680000,2505147019375
%N Denominator of n^(n-2)/n!.
%C Denominators 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
%C Absolute value of denominator of the coefficient of 1/(n*x-1) in the partial fraction decomposition of 1/(x-1)*1/(2*x-1)*...*1/(n*x-1). [Joris Roos (jorisr(AT)gmx.de), Aug 02 2009]
%H G. C. Greubel, <a href="/A036503/b036503.txt">Table of n, a(n) for n = 1..450</a>
%e 1, 1/2, 1/2, 2/3, 25/24, 9/5, 2401/720, 2048/315, 59049/4480, 15625/567, 214358881/3628800, ...
%t Denominator[Table[n^(n - 2)/n!, {n, 1, 50}]] (* _G. C. Greubel_, Nov 14 2017 *)
%o (PARI) for(n=1, 50, print1(denominator(n^(n-2)/n!), ", ")) \\ _G. C. Greubel_, Nov 14 2017
%o (Magma) [Denominator(n^(n - 2)/Factorial(n)): n in [1..50]]; // _G. C. Greubel_, Nov 14 2017
%Y Cf. A036502, A036504.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_
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