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%I #10 Jul 14 2014 17:02:02
%S -1,6,33,380,3535,189714,285929,319735800,1160703963,145739620510,
%T 86294277091,10914811650686580,60229285882649,163637596919801624970,
%U 3392462704290802545,669084376596453009616,370468452361579892135179,157145213515550643044429571846
%N Numerator of PolyLog[ -n, 1/n ].
%C PolyLog[n,z] = Sum[ z^k/k^n, {k,1,Infinity} ]. PolyLog[ -n,1/n] = Sum[ k^n/n^k, {k,1,Infinity}] for n>1. n divides a(n). p^k divides a(p^k) for all prime p and integer k>0. p^k divides a(p^k-1) for prime p>2 and integer k>0.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>.
%F a(n) = Numerator[ PolyLog[ -n, 1/n ] ]. For n>1 a(n) = Numerator[ (-1)^n * PolyLog[ -n, n ] ].
%F For n>1, a(n) is the numerator of n*A122778(n)/(n-1)^(n+1) = Sum[k=0..n] A(n,k)*n^(k+1)/(n-1)^(n+1). For n>1, a(n) = n * A122778(n)/gcd(A122778(n),(n-1)^(n+1)). - _Max Alekseyev_, Sep 11 2006
%e PolyLog[ -n,1/n] begins -1/12, 6, 33/8, 380/81, 3535/512, 189714/15625, ...
%t Numerator[Table[PolyLog[ -n,1/n],{n,1,40}]]
%o (PARI) a(n)=numerator(polylog(-n,1/n)) \\ _Charles R Greathouse IV_, Jul 14 2014
%Y Cf. A119758.
%K frac,sign
%O 1,2
%A _Alexander Adamchuk_, Sep 06 2006
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