A212847 Polylogarithm li(-n,-2/3) multiplied by (5^(n+1))/3.

1, -2, -2, 22, 94, -890, -9170, 67030, 1495870, -6581210, -362016050, 194447350, 120002960350, 554823694150, -51277487618450, -601106981110250, 26775789844186750, 591304973974171750, -16113120605399179250

Offset

0,2

Comments

See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=2,q=3.

Links

Stanislav Sykora, Table of n, a(n) for n = 0..100

Formula

See formula in A212846, setting p=2,q=3.

From Vaclav Kotesovec, May 17 2022: (Start)

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)

Example

polylog(-5,-2/3)*5^6/3 = -890.

Mathematica

f[n_] := PolyLog[-n, -2/3] 5^(n + 1)/3; f[0] = 1; Array[f, 20, 0] (* Robert G. Wilson v, Dec 25 2015 *)

Prog

(PARI) \\ See A212846; run limnpq(nmax, 2, 3)

Crossrefs

Cf. A212846 (li(-n,-1/2)), A210246 (li(-n,-1/3)).

Cf. A213127 through A213157.

Sequence in context: A143807 A118454 A118326 * A087405 A357244 A001012

Adjacent sequences: A212844 A212845 A212846 * A212848 A212849 A212850

Keyword

sign

Author

Stanislav Sykora, May 28 2012

Status

approved