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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.

2

`%I #12 Oct 24 2012 19:16:59
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`%S 1,0,1,3,0,1,54,9,0,1,3861,216,18,0,1,1028700,19305,540,30,0,1,
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`%T 1067510583,6172200,57915,1080,45,0,1,4390552197234,7472574081,
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`%U 21602700,135135,1890,63,0,1,72022439672173161,35124417577872,29890296324,57607200,270270,3024,84,0,1
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`%N 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.
`

`%C Column k=0 is A054545.
`

`%F E.g.f.: exp(y*x)*A(x) where A(x) is the e.g.f. for A054545.
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`%e 1;
`

`%e 0, 1;
`

`%e 3, 0, 1;
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`%e 54, 9, 0, 1;
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`%e 3861, 216, 18, 0, 1;
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`%e 1028700, 19305, 540, 30, 0, 1;
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`%e 1067510583, 6172200, 57915, 1080, 45, 0, 1;
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`%t 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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`%K nonn,tabl
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`%O 0,4
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`%A _Geoffrey Critzer_, Oct 07 2012
`