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A054545
Number of labeled digraphs on n unisolated nodes (inverse binomial transform of A053763).
4
1, 0, 3, 54, 3861, 1028700, 1067510583, 4390552197234, 72022439672173161, 4721718122762915558520, 1237892818862615769794806443, 1298060597552993036455274183624814, 5444502293926142814638982021027945429501, 91343781554550362267223855965291602454111295060
OFFSET
0,3
LINKS
N. J. A. Sloane, Transforms
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*2^(k*(k-1)).
EXAMPLE
2^(n*(n-1))=1+3*C(n,2)+54*C(n,3)+3861*C(n,4)+...
MATHEMATICA
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 *)
PROG
(PARI) a(n)={sum(k=0, n, (-1)^(n-k)*binomial(n, k)*2^(k*(k-1)))} \\ Andrew Howroyd, Nov 07 2019
CROSSREFS
Cf. A006129.
Sequence in context: A006025 A049414 A003027 * A158103 A174579 A171739
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Apr 09 2000
EXTENSIONS
Terms a(12) and beyond from Andrew Howroyd, Nov 07 2019
STATUS
approved