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A256194 a(n) = denominator of n!*n^n*Product_{k=0..n} 1/(n*k + n - 1).

%I A256194 #13 Sep 26 2018 12:26:23
%S A256194 15,440,21945,277704,178986115,215289360,107174712645,2019114114160,
%T A256194 5162399729063577,310327149656160,264020420256172514935,
%U A256194 555320997799108800,183986274976015448239875,7616449380979972355121376,132186242095677958872242925,3493664585524176681103200
%N A256194 a(n) = denominator of n!*n^n*Product_{k=0..n} 1/(n*k + n - 1).
%C A256194 n!*n^n*Product_{k=0..n} 1/(n*k + n - 1) = Sum_{k=0..n} (-1)^k*binomial(n,k)/(n*k + n - 1) (see arXiv link).
%H A256194 Brett Pansano, <a href="http://arxiv.org/abs/1503.04678">An Interesting Identity</a>, arXiv:1503.04678 [math.GM], 2015.
%t A256194 Table[Denominator[n! n^n Product[1/(n k + n - 1), {k, 0, n}]], {n, 2, 17}] (* _Jean-François Alcover_, Sep 26 2018 *)
%o A256194 (PARI) a(n) = denominator(sum(k=0, n, (-1)^k*binomial(n,k)/(n*k+n-1)));
%Y A256194 Cf. A145921 (numerators).
%K A256194 nonn,frac
%O A256194 2,1
%A A256194 _Michel Marcus_, Mar 19 2015