OFFSET
0,3
COMMENTS
See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=1,q=8.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..100
OEIS-Wiki, Eulerian polynomials
FORMULA
See formula in A212846, setting p=1,q=8.
E.g.f.: 9/(8+exp(9*x)). [Joerg Arndt, Apr 21 2013]
a(n) = Sum_{k=0..n} k! * (-1)^k * 9^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022
EXAMPLE
polylog(-5,-1/8)*9^6/8 = 5199.
MAPLE
seq(add((-1)^(n-k)*combinat[eulerian1](n, k)*8^k, k=0..n), n=0..17); # Peter Luschny, Apr 21 2013
MATHEMATICA
Table[If[n == 0, 1, PolyLog[-n, -1/8] 9^(n+1)/8], {n, 0, 19}] (* Jean-François Alcover, Jun 27 2019 *)
PROG
(PARI) /* See A212846; run limnpq(nmax, 1, 8) */
(PARI) x='x+O('x^66); Vec(serlaplace( 9/(8+exp(9*x)) )) \\ Joerg Arndt, Apr 21 2013
(PARI) a(n) = sum(k=0, n, k!*(-1)^k*9^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Stanislav Sykora, Jun 06 2012
STATUS
approved