# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a121376 Showing 1-1 of 1 %I A121376 #10 Jul 14 2014 17:02:02 %S A121376 -1,6,33,380,3535,189714,285929,319735800,1160703963,145739620510, %T A121376 86294277091,10914811650686580,60229285882649,163637596919801624970, %U A121376 3392462704290802545,669084376596453009616,370468452361579892135179,157145213515550643044429571846 %N A121376 Numerator of PolyLog[ -n, 1/n ]. %C A121376 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 A121376 Eric Weisstein's World of Mathematics, Polylogarithm. %F A121376 a(n) = Numerator[ PolyLog[ -n, 1/n ] ]. For n>1 a(n) = Numerator[ (-1)^n * PolyLog[ -n, n ] ]. %F A121376 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 A121376 PolyLog[ -n,1/n] begins -1/12, 6, 33/8, 380/81, 3535/512, 189714/15625, ... %t A121376 Numerator[Table[PolyLog[ -n,1/n],{n,1,40}]] %o A121376 (PARI) a(n)=numerator(polylog(-n,1/n)) \\ _Charles R Greathouse IV_, Jul 14 2014 %Y A121376 Cf. A119758. %K A121376 frac,sign %O A121376 1,2 %A A121376 _Alexander Adamchuk_, Sep 06 2006 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE