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A217580
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Triangular array read by rows. T(n,k) is the number of labeled digraphs on n nodes with exactly k isolated nodes. 0<=k<=n.
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2
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1, 0, 1, 3, 0, 1, 54, 9, 0, 1, 3861, 216, 18, 0, 1, 1028700, 19305, 540, 30, 0, 1, 1067510583, 6172200, 57915, 1080, 45, 0, 1, 4390552197234, 7472574081, 21602700, 135135, 1890, 63, 0, 1, 72022439672173161, 35124417577872, 29890296324, 57607200, 270270, 3024, 84, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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E.g.f.: exp(y*x)*A(x) where A(x) is the e.g.f. for A054545.
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EXAMPLE
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1;
0, 1;
3, 0, 1;
54, 9, 0, 1;
3861, 216, 18, 0, 1;
1028700, 19305, 540, 30, 0, 1;
1067510583, 6172200, 57915, 1080, 45, 0, 1;
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MATHEMATICA
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nn=6; s=Sum[2^(2 Binomial[n, 2])x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[Exp[y x] s/Exp[x], {x, 0, nn}], {x, y}] //Grid
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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