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

0,2

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).

Links

Table of n, a(n) for n=0..15.

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

Example

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

Mathematica

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

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).

Sequence in context: A053891 A053897 A017294 * A134631 A036511 A263386

Adjacent sequences: A273695 A273696 A273697 * A273699 A273700 A273701

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 28 2016

Status

approved