A266581 Numerators of expansion of PolyLog(-2, x)/PolyLog(2, x), where PolyLog(m, x) is the polylogarithm function.

1, 15, 1145, 7795, 10605889, 59526571, 139954552433, 34217723087, 806539298609929, 3932874930141827, 4100492004734957581, 96658551584623754987, 838219558485468722155050481, 142916593419748754034403361, 158366688967470905539833679601, 102317913027622943383626250477

Offset: 0

Author

Ilya Gutkovskiy, May 07 2016

Keywords

• nonn
• frac

Comments

Numerators of expansion of (Sum_{k>=1} x^k*k^2)/(Sum_{k>=1} x^k/k^2).

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).

Examples

			1, 15/4, 1145/144, 7795/576, 10605889/518400, 59526571/2073600, 139954552433/3657830400, 34217723087/696729600, 806539298609929/13168189440000, …
		

Links

• Eric Weisstein's World of Mathematics, Dilogarithm, Polylogarithm, and Wolstenholme Number

Crossrefs

Cf. A232193 (numerators of expansion of PolyLog(-1, x)/PolyLog(1, x)), A232248 (denominators of expansion of PolyLog(-1, x)/PolyLog(1, x)).

Cf. A000330, A007406, A007407, A273698 (denominators).

Programs

Mathematica

Table[Numerator[SeriesCoefficient[PolyLog[-2, x]/PolyLog[2, x], {x, 0, n}]], {n, 0, 15}]