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 A266581 #27 Feb 16 2025 08:33:28
%S A266581 1,15,1145,7795,10605889,59526571,139954552433,34217723087,
%T A266581 806539298609929,3932874930141827,4100492004734957581,
%U A266581 96658551584623754987,838219558485468722155050481,142916593419748754034403361,158366688967470905539833679601,102317913027622943383626250477
%N A266581 Numerators of expansion of PolyLog(-2, x)/PolyLog(2, x), where PolyLog(m, x) is the polylogarithm function.
%C A266581 Numerators of expansion of (Sum_{k>=1} x^k*k^2)/(Sum_{k>=1} x^k/k^2).
%C A266581 Numerators 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 A266581 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Dilogarithm.html">Dilogarithm</a>, <a href="https://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>, and <a href="https://mathworld.wolfram.com/WolstenholmeNumber.html">Wolstenholme Number</a>
%e A266581 1, 15/4, 1145/144, 7795/576, 10605889/518400, 59526571/2073600, 139954552433/3657830400, 34217723087/696729600, 806539298609929/13168189440000, …
%t A266581 Table[Numerator[SeriesCoefficient[PolyLog[-2, x]/PolyLog[2, x], {x, 0, n}]], {n, 0, 15}]
%Y A266581 Cf. A232193 (numerators of expansion of PolyLog(-1, x)/PolyLog(1, x)), A232248 (denominators of expansion of PolyLog(-1, x)/PolyLog(1, x)).
%Y A266581 Cf. A000330, A007406, A007407, A273698 (denominators).
%K A266581 nonn,frac
%O A266581 0,2
%A A266581 _Ilya Gutkovskiy_, May 07 2016