This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A121376 #24 Feb 16 2025 08:33:02
%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).
%H A121376 Thomas Scheuerle, <a href="/A121376/b121376.txt">Table of n, a(n) for n = 1..150</a>
%H A121376 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>.
%F A121376 a(n) = numerator( PolyLog( -n, 1/n ) ). For n>1 a(n) = numerator( (-1)^n * PolyLog( -n, n ) ).
%F A121376 PolyLog(-n, 1/n) = a(n)/A121985(n) = Sum_{k>=1} k^n/n^k, 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. Also PolyLog(n, z) = Sum_{k>=1} z^k/k^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)=if(n==1,-1,numerator(polylog(-n,1/n))) \\ _Charles R Greathouse IV_, Jul 14 2014
%Y A121376 Cf. A121985 (denominator).
%Y A121376 Cf. A119758.
%K A121376 frac,sign
%O A121376 1,2
%A A121376 _Alexander Adamchuk_, Sep 06 2006