A273698 Denominators of expansion of PolyLog(-2, x)/PolyLog(2, x), where PolyLog(m, x) is the polylogarithm function.

1, 4, 144, 576, 518400, 2073600, 3657830400, 696729600, 13168189440000, 52672757760000, 45888506560512000, 917770131210240000, 6840049010896797696000000, 1013340594206932992000000, 984967057569138868224000000, 562838318610936496128000000

Offset: 0

Author

Ilya Gutkovskiy, May 28 2016

Keywords

• nonn
• frac

Comments

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

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).

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, A266581 (numerators).

Programs

Mathematica

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