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%I #10 Jan 19 2024 20:16:22
%S 1,8,81,2048,15625,6718464,5764801,2147483648,31381059609,
%T 64000000000000,3138428376721,2218611106740436992,3937376385699289,
%U 1115112108958398021632,39903080760955810546875,604462909807314587353088,14063084452067724991009,16918235275724100929608539439104
%N Numerator of n*B(n,1+1/n), where B(.,.) is the Beta Function.
%C n*B(n,1+1/n) = Gamma(n+1)*Gamma(1+1/n)/Gamma(1+n+1/n) is the integral over F(n)=[1-x^(1/n)]^(1/n) from x=0 to 1.
%e The fractions are 1/2, 8/15, 81/140, 2048/3315, 15625/24024, ...
%p seq( numer(n*Beta(n,1+1/n)),n=1..30) ;
%t Table[Numerator[n Beta[n, 1 + 1/n]], {n, 1, 15}] (* _Jean-François Alcover_, Sep 26 2018 *)
%o (Derive) VECTOR(NUMERATOR(F(n)), n, 1, 10)
%K nonn,frac
%O 1,2
%A Jose Luis (jl_altamirano(AT)yahoo.com), Oct 25 2008
%E Definition clarified by _R. J. Mathar_, Dec 08 2008