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A295182
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a(n) = n! * [x^n] exp(-n*x)/(1 - x)^n.
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3
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1, 0, 2, 6, 72, 620, 8640, 122346, 2156672, 41367672, 905126400, 21646532270, 570077595648, 16268377195044, 502096929431552, 16629319748711250, 588938142209310720, 22196966267762213744, 887352465220427317248, 37496112562144553167062, 1670071417348195942400000, 78195398849926292810318940
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OFFSET
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0,3
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COMMENTS
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The n-th term of the n-fold exponential convolution of A000166 with themselves.
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LINKS
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FORMULA
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a(n) ~ phi^(3*n - 1/2) * n^n / (5^(1/4) * exp(n*(1 + 1/phi))), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Nov 16 2017
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MAPLE
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S:= series((exp(-x)/(1-x))^n, x, 30):
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MATHEMATICA
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Table[n! SeriesCoefficient[Exp[-n x]/(1 - x)^n, {x, 0, n}], {n, 0, 21}]
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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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