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A370226
a(n) = n!^2 * [x^n] polylog(2,x)^4.
3
0, 0, 0, 0, 576, 14400, 424800, 16405200, 827179584, 53370793728, 4311612000000, 427527300499200, 51134102684222976, 7266620131443459072, 1211052516384021083136, 234033301581064751001600, 51924413277653839769124864, 13111663349134716037934874624, 3739245464888523341104099885056
OFFSET
0,5
COMMENTS
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).
LINKS
Vaclav Kotesovec, Recurrence (of order 10)
Eric Weisstein's World of Mathematics, Polylogarithm.
Wikipedia, Polylogarithm.
FORMULA
a(n)/(n!)^2 ~ Pi^6 / (54*n^2).
MATHEMATICA
CoefficientList[Series[PolyLog[2, x]^4, {x, 0, 20}], x] * Range[0, 20]!^2
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}]
CROSSREFS
Sequence in context: A209781 A330840 A226285 * A354021 A282780 A268638
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 12 2024
STATUS
approved