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A361527
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Triangular array read by rows. T(n,k) is the number of labeled digraphs on [n] having exactly k strongly connected components all of which are simple cycles, n >= 0, 0 <= k <= n.
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1
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1, 0, 1, 0, 1, 3, 0, 2, 21, 25, 0, 6, 213, 774, 543, 0, 24, 3470, 30275, 59830, 29281, 0, 120, 95982, 1847265, 7757355, 10110735, 3781503, 0, 720, 4578588, 190855000, 1522899105, 3944546095, 3767987307, 1138779265
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OFFSET
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0,6
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COMMENTS
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Here, a strongly connected component containing exactly 1 vertex is considered a cycle.
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LINKS
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EXAMPLE
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1;
0, 1;
0, 1, 3;
0, 2, 21, 25;
0, 6, 213, 774, 543;
0, 24,3470, 30275, 59830, 29281;
...
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MATHEMATICA
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nn = 7;
a[x_] := Log[1/(1 - x)];
begfa =Total[CoefficientList[ Series[1/(Total[ CoefficientList[Series[ Exp[-u *a[x]], {x, 0, nn}], x]* Table[z^n/(2^Binomial[n, 2]), {n, 0, nn}]]), {z, 0, nn}], z]*Table[z^n 2^Binomial[n, 2], {n, 0, nn}]];
Table[Take[(Range[0, nn]! CoefficientList[begfa, {z, u}])[[i]], i], {i, 1, nn + 1}] // 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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