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A213129
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Polylogarithm li(-n,-1/6) multiplied by (7^(n+1))/6.
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4
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1, -1, -5, -13, 115, 2099, 11395, -177373, -5116685, -40481581, 948973795, 36701972867, 375364322515, -12090607539661, -580544884927805, -7188739235243293, 301374306966657715, 17150539711123411859, 246564346727945106595, -12988846468460187345853
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OFFSET
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0,3
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COMMENTS
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See the sequence A212846 which describes the general case of li(-n,-p/q). This sequence is obtained for p=1,q=6.
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LINKS
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FORMULA
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See formula in A212846, setting p=1,q=6.
a(n) = Sum_{k=0..n} k! * (-1)^k * 7^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022
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EXAMPLE
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polylog(-5,-1/6)*7^6/6 = 2099.
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MAPLE
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seq(add((-1)^(n-k)*combinat[eulerian1](n, k)*6^k, k=0..n), n=0..17); # Peter Luschny, Apr 21 2013
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MATHEMATICA
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PROG
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(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
(PARI) a(n) = sum(k=0, n, k!*(-1)^k*7^(n-k)*stirling(n, k, 2)); \\ Seiichi Manyama, Mar 13 2022
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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