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 A213127 Polylogarithm li(-n,-1/4) multiplied by (5^(n+1))/4. 35
 1, -1, -3, -1, 69, 455, -1155, -50065, -334155, 4107095, 112058925, 491352575, -24429589275, -535893782425, 606194735325, 249291355871375, 4380933801391125, -56204145098271625, -4031655689182933875 (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=4. 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=4 From Peter Bala, Jun 24 2012: (Start) E.g.f.: A(x) = 5/(4 + exp(5*x)) = 1 - x - 3*x^2/2! - x^3/3! + 69*x^4/4! + .... The compositional inverse (A(-x) - 1)^(-1) = x + 3*x^2/2 + 13*x^3/3 + 51*x^4/4 + 205*x^5/5 + ... is the logarithmic generating function for A015521. (End) G.f.: 1/Q(0), where Q(k) = 1 + x*(k+1)/( 1 - 4*x*(k+1)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Dec 17 2013 EXAMPLE polylog(-5,-1/4)*5^6/4 = 455 MAPLE seq(add((-1)^(n-k)*combinat[eulerian1](n, k)*4^k, k=0..n), n=0..18); # Peter Luschny, Apr 21 2013 MATHEMATICA a[0] = 1; a[n_] := PolyLog[-n, -1/4] * 5^(n+1)/4; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jul 29 2018 *) PROG (PARI) /* see A212846; run limnpq(nmax, 1, 4) */ (PARI) x='x+O('x^66); Vec(serlaplace( 5/(4+exp(5*x)) )) \\ Joerg Arndt, Apr 21 2013 CROSSREFS Cf. A212846, A210246, A212847, A213128 through A213157. A015521. Sequence in context: A189898 A082525 A162221 * A213069 A266277 A016482 Adjacent sequences:  A213124 A213125 A213126 * A213128 A213129 A213130 KEYWORD sign AUTHOR Stanislav Sykora, Jun 06 2012 STATUS approved

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Last modified November 15 22:20 EST 2018. Contains 317252 sequences. (Running on oeis4.)