A304581 Numerator of Sum_{k=1..n-1} 1/(k*(n-k))^2.

0, 0, 1, 1, 41, 13, 8009, 161, 190513, 167101, 13371157, 21857, 316786853, 371449, 52598187029, 260957190289, 129548894873, 3562512061, 295728132584141, 814542451061, 105590441859671453, 21013691164284241, 2988054680665783, 5623939943287, 1567371864703176307

Offset: 0

Author

Vaclav Kotesovec, May 15 2018

Keywords

• nonn
• frac

Comments

Sum_{k=1..n-1} 1/(k*(n-k))^2 is asymptotic to Pi^2/(3*n^2) + 4*log(n)/n^3.

Examples

			0, 0, 1, 1/2, 41/144, 13/72, 8009/64800, 161/1800, 190513/2822400, ...
		

Links

• Eric Weisstein's World of Mathematics, Dilogarithm.
• Eric Weisstein's World of Mathematics, Polylogarithm.

Crossrefs

Cf. A002547, A304582, A302827.

Programs

Mathematica

CoefficientList[Series[PolyLog[2, x]^2, {x, 0, 25}], x]//Numerator
Table[Sum[1/(k*(n - k))^2, {k, 1, n - 1}], {n, 0, 25}]//Numerator