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A212847
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Polylogarithm li(-n,-2/3) multiplied by (5^(n+1))/3.
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35
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1, -2, -2, 22, 94, -890, -9170, 67030, 1495870, -6581210, -362016050, 194447350, 120002960350, 554823694150, -51277487618450, -601106981110250, 26775789844186750, 591304973974171750, -16113120605399179250
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OFFSET
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0,2
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COMMENTS
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See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=2,q=3.
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LINKS
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FORMULA
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See formula in A212846, setting p=2,q=3.
E.g.f.: 5/(3 + 2*exp(5*x)).
a(n) ~ n! * 2*(log(3/2) * cos(n*arctan(Pi/log(3/2))) - Pi * sin(n*arctan(Pi/log(3/2)))) * 5^(n+1) / (3 * (Pi^2 + log(3/2)^2)^(1 + n/2)). (End)
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EXAMPLE
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polylog(-5,-2/3)*5^6/3 = -890.
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MATHEMATICA
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f[n_] := PolyLog[-n, -2/3] 5^(n + 1)/3; f[0] = 1; Array[f, 20, 0] (* Robert G. Wilson v, Dec 25 2015 *)
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PROG
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See (PARI) in A212846; run limnpq(nmax, 2, 3)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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