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A182661
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Expansion of x^3*exp(-x)/(3*(1-x)).
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1
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2, 0, 20, 80, 630, 4928, 44520, 444960, 4894890, 58738240, 763597692, 10690366960, 160355505310, 2565688083840, 43616697426640, 785100553677888, 14916910519881810, 298338210397633920, 6265102418350314980, 137832253203706926480
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OFFSET
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3,1
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COMMENTS
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a(n) is the number of 3-cycles in all derangements of {1,2,...n}.
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LINKS
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FORMULA
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E.g.f.: x^3 * exp(-x)/(3*(1-x)).
In general, E.g.f. for the number of k cycles in the derangements of [n] is: x^k * exp(-x)/(k*(1-x)).
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MAPLE
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egf:= x^3 * exp(-x)/(3*(1-x)):
a:= n-> n! * coeff (series (egf, x, n+1), x, n):
seq (a(n), n=3..25);
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MATHEMATICA
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Table[Count[Flatten[Map[Length, Map[ToCycles, Derangements[n]], {2}]], 3], {n, 0, 8}]
Range[0, 20]! CoefficientList[Series[x^3/3 Exp[-x]/(1-x), {x, 0, 20}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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