A213128 Polylogarithm li(-n,-1/5) multiplied by (6^(n+1))/5.
1, -1, -4, -6, 96, 1104, 2016, -112176, -1718784, -642816, 437031936, 7656021504, -24274059264, -3939918299136, -72733516959744, 699443277686784, 67781787782086656, 1236409075147014144, -25430445045847425024
Offset: 0
Keywords
Examples
polylog(-5,-1/5)*6^6/5 = 1104.
Links
- Stanislav Sykora, Table of n, a(n) for n = 0..100
- OEIS-Wiki, Eulerian polynomials
Programs
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Maple
seq(add((-1)^(n-k)*combinat[eulerian1](n,k)*5^k, k=0..n),n=0..18); # Peter Luschny, Apr 21 2013
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Mathematica
Table[If[n == 0, 1, PolyLog[-n, -1/5] 6^(n+1)/5], {n, 0, 18}] (* Jean-François Alcover, Jun 29 2019 *) -
PARI
/*See A212846; run limnpq(nmax,1,5) */
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PARI
x='x+O('x^66); Vec(serlaplace( 6/(5+exp(6*x)) )) \\ Joerg Arndt, Apr 21 2013 -
PARI
a(n) = sum(k=0, n, k!*(-1)^k*6^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022
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
a(n) = Sum_{k=0..n} k! * (-1)^k * 6^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022
Comments