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%I #10 Jun 26 2016 07:45:41
%S 1,4,144,576,518400,2073600,3657830400,696729600,13168189440000,
%T 52672757760000,45888506560512000,917770131210240000,
%U 6840049010896797696000000,1013340594206932992000000,984967057569138868224000000,562838318610936496128000000
%N Denominators of expansion of PolyLog(-2, x)/PolyLog(2, x), where PolyLog(m, x) is the polylogarithm function.
%C Denominators of expansion of (Sum_{k>=1} x^k*k^2)/(Sum_{k>=1} x^k/k^2).
%C Denominators of numbers for which convolution with Sum_{k=1..n} 1/k^2 = A007406(n)/A007407(n) gives Sum_{k=1..n} k^2 = A000330(n).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Dilogarithm.html">Dilogarithm</a>, <a href="http://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>, and <a href="http://mathworld.wolfram.com/WolstenholmeNumber.html">Wolstenholme Number</a>
%e 1, 15/4, 1145/144, 7795/576, 10605889/518400, 59526571/2073600, 139954552433/3657830400, 34217723087/696729600, 806539298609929/13168189440000, ...
%t Table[Denominator[SeriesCoefficient[PolyLog[-2, x]/PolyLog[2, x], {x, 0, n}]], {n, 0, 15}]
%Y Cf. A232193 (numerators of expansion of PolyLog(-1, x)/PolyLog(1, x)), A232248 (denominators of expansion of PolyLog(-1, x)/PolyLog(1, x)).
%Y Cf. A000330, A007406, A007407, A266581 (numerators).
%K nonn,frac
%O 0,2
%A _Ilya Gutkovskiy_, May 28 2016