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 A213129 Polylogarithm li(-n,-1/6) multiplied by (7^(n+1))/6. 3
 1, -1, -5, -13, 115, 2099, 11395, -177373, -5116685, -40481581, 948973795, 36701972867, 375364322515, -12090607539661, -580544884927805, -7188739235243293, 301374306966657715, 17150539711123411859, 246564346727945106595, -12988846468460187345853 (list; graph; refs; listen; history; text; internal format)
 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=6. 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=6. E.g.f.: 7/(6+exp(7*x)). [Joerg Arndt, Apr 21 2013] EXAMPLE polylog(-5,-1/6)*7^6/6 = 2099. MAPLE seq(add((-1)^(n-k)*combinat[eulerian1](n, k)*6^k, k=0..n), n=0..17); # Peter Luschny, Apr 21 2013 MATHEMATICA Table[If[n == 0, 1, PolyLog[-n, -1/6] 7^(n+1)/6], {n, 0, 19}] (* Jean-François Alcover, Jun 27 2019 *) PROG (PARI) /* See A212846; run limnpq(nmax, 1, 6) */ (PARI) x='x+O('x^66); Vec(serlaplace( 7/(6+exp(7*x)) )) \\ Joerg Arndt, Apr 21 2013 CROSSREFS Cf. A212846, A210246, A212847, A213127, A213128, Cf. A213130 through A213157 Sequence in context: A228280 A155175 A155185 * A004063 A005764 A305643 Adjacent sequences:  A213126 A213127 A213128 * A213130 A213131 A213132 KEYWORD sign AUTHOR Stanislav Sykora, Jun 06 2012 STATUS approved

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)