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A054545
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Number of labeled digraphs on n unisolated nodes (inverse binomial transform of A053763).
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4
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1, 0, 3, 54, 3861, 1028700, 1067510583, 4390552197234, 72022439672173161, 4721718122762915558520, 1237892818862615769794806443, 1298060597552993036455274183624814, 5444502293926142814638982021027945429501, 91343781554550362267223855965291602454111295060
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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) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*2^(k*(k-1)).
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EXAMPLE
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2^(n*(n-1))=1+3*C(n,2)+54*C(n,3)+3861*C(n,4)+...
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MATHEMATICA
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nn=20; s=Sum[2^(2Binomial[n, 2])x^n/n!, {n, 0, nn}]; Range[0, nn]!CoefficientList[Series[ s/Exp[x], {x, 0, nn}], x] (* Geoffrey Critzer, Oct 07 2012 *)
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PROG
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(PARI) a(n)={sum(k=0, n, (-1)^(n-k)*binomial(n, k)*2^(k*(k-1)))} \\ Andrew Howroyd, Nov 07 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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