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A346409
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a(n) = (n!)^2 * Sum_{k=0..n-1} (-1)^k / ((n-k)^2 * k!).
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1
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0, 1, -3, 13, -52, 476, 1344, 156192, 6935424, 470168064, 38948065920, 3979380286080, 489922581219840, 71586095491054080, 12249193741572372480, 2426646293132502067200, 551096248249459158220800, 142236660450422499604070400, 41404182857569072540171468800
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OFFSET
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0,3
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LINKS
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FORMULA
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Sum_{n>=0} a(n) * x^n / (n!)^2 = polylog(2,x) * exp(-x).
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MATHEMATICA
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Table[(n!)^2 Sum[(-1)^k/((n - k)^2 k!), {k, 0, n - 1}], {n, 0, 18}]
nmax = 18; CoefficientList[Series[PolyLog[2, x] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!^2
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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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