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A318616
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a(n) = n! * [x^n] (1 - x)^(n*x).
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1
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1, 0, -4, -9, 160, 1350, -14904, -335160, 1796096, 125615448, 204300000, -64591072920, -735003528192, 41673388751280, 1113912529707264, -30043364514345000, -1703374149711298560, 17822402097051182400, 2856178489894627203072, 12394040043610922716800, -5255899207995216384000000
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history;
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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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a(n) = n! * [x^n] exp(-n*x*Sum_{k>=1} x^k/k).
a(n) = n! * Sum_{k=0..n} (-1)^k*n^(n-k)*Stirling1(k,n-k)/k!.
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MATHEMATICA
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Table[n! SeriesCoefficient[(1 - x)^(n x), {x, 0, n}], {n, 0, 20}]
Join[{1}, Table[n! Sum[(-1)^k n^(n - k) StirlingS1[k, n - k]/k!, {k, n}], {n, 20}]]
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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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