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A213132
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Polylogarithm li(-n,-1/9) multiplied by (10^(n+1))/9.
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4
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1, -1, -8, -46, 64, 7280, 118720, 406160, -35578880, -1156775680, -12796467200, 444964083200, 27457634713600, 594958346547200, -9096689344716800, -1258068242084608000, -45330583283597312000, 24150498582339584000, 95678058298287259648000, 5379182782796767182848000
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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=9.
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LINKS
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FORMULA
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See formula in A212846, setting p=1,q=9.
a(n) = Sum_{k=0..n} k! * (-1)^k * 10^(n-k) * Stirling2(n,k). - Seiichi Manyama, Mar 13 2022
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EXAMPLE
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polylog(-5, -1/9)*10^6/9 = 7280.
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MAPLE
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seq(add((-1)^(n-k)*combinat[eulerian1](n, k)*9^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, 9) */
(PARI) x='x+O('x^66); Vec(serlaplace( 10/(9+exp(10*x)) )) \\ Joerg Arndt, Apr 21 2013
(PARI) a(n) = sum(k=0, n, k!*(-1)^k*10^(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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