%I #8 Feb 13 2024 04:52:40
%S 0,0,0,0,576,14400,424800,16405200,827179584,53370793728,
%T 4311612000000,427527300499200,51134102684222976,7266620131443459072,
%U 1211052516384021083136,234033301581064751001600,51924413277653839769124864,13111663349134716037934874624,3739245464888523341104099885056
%N a(n) = n!^2 * [x^n] polylog(2,x)^4.
%C In general, for m >= 1, [x^n] polylog(2,x)^m ~ m*zeta(2)^(m-1)/n^2 = m * Pi^(2*m-2) / (6^(m-1) * n^2).
%H Vaclav Kotesovec, <a href="/A370226/b370226.txt">Table of n, a(n) for n = 0..250</a>
%H Vaclav Kotesovec, <a href="/A370226/a370226.txt">Recurrence (of order 10)</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Polylogarithm.html">Polylogarithm</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Polylogarithm">Polylogarithm</a>.
%F a(n)/(n!)^2 ~ Pi^6 / (54*n^2).
%t CoefficientList[Series[PolyLog[2, x]^4, {x, 0, 20}], x] * Range[0, 20]!^2
%t Table[n!^2 * Sum[Sum[1/(k*(j-k))^2, {k, 1, j-1}] * Sum[1/(k*(n-j-k))^2, {k, 1, n-j-1}], {j, 1, n-1}], {n, 0, 20}]
%Y Cf. A302827, A370225.
%K nonn
%O 0,5
%A _Vaclav Kotesovec_, Feb 12 2024
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