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 A213128 Polylogarithm li(-n,-1/5) multiplied by (6^(n+1))/5. 4
 1, -1, -4, -6, 96, 1104, 2016, -112176, -1718784, -642816, 437031936, 7656021504, -24274059264, -3939918299136, -72733516959744, 699443277686784, 67781787782086656, 1236409075147014144, -25430445045847425024 (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=5. 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=5 From Peter Bala, Jun 24 2012: (Start) E.g.f.: A(x) = 6/(5 + exp(6*x)) = 1 - x - 4*x^2/2! - 6 x^3/3! + 96*x^4/4! + .... The compositional inverse (A(-x) - 1)^(-1) = x + 4*x^2/2 + 21*x^3/3 + 104*x^4/4 + 521*x^5/5 + ... is the logarithmic generating function for A015531. (End) G.f.: 1/Q(0), where Q(k) = 1 + x*(k+1)/( 1 - 5*x*(k+1)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Dec 17 2013 EXAMPLE polylog(-5,-1/5)*6^6/5 = 1104 MAPLE seq(add((-1)^(n-k)*combinat[eulerian1](n, k)*5^k, k=0..n), n=0..18); # Peter Luschny, Apr 21 2013 PROG (PARI) /*See A212846; run limnpq(nmax, 1, 5) */ (PARI) x='x+O('x^66); Vec(serlaplace( 6/(5+exp(6*x)) )) \\ Joerg Arndt, Apr 21 2013 CROSSREFS Cf. A212846, A210246, A212847, A213127 Cf. A213129 through A213157. Cf. A015531. Sequence in context: A222495 A087934 A052684 * A105037 A139730 A013023 Adjacent sequences:  A213125 A213126 A213127 * A213129 A213130 A213131 KEYWORD sign AUTHOR Stanislav Sykora, Jun 06 2012 STATUS approved

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Last modified December 16 07:12 EST 2018. Contains 318158 sequences. (Running on oeis4.)