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

0,2

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).

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[Numerator[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, A273698 (denominators).

Sequence in context: A129764 A027552 A212857 * A337677 A098210 A090213

Adjacent sequences: A266578 A266579 A266580 * A266582 A266583 A266584

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 07 2016

Status

approved