A054547
Triangular array giving number of labeled digraphs on n unisolated nodes and k=0..n*(n-1) arcs.
Original entry on oeis.org
0, 0, 2, 1, 0, 0, 12, 20, 15, 6, 1, 0, 0, 12, 140, 435, 768, 920, 792, 495, 220, 66, 12, 1, 0, 0, 0, 240, 2520, 11604, 34150, 73560, 123495, 166860, 184426, 167900, 125965, 77520, 38760, 15504, 4845, 1140, 190, 20, 1
Offset: 1
Triangle T(n,k) begins:
[0],
[0,2,1],
[0,0,12,20,15,6,1],
[0,0,12,140,435,768,920,792,495,220,66,12,1],
...
-
row(n) = {Vecrev(sum(i=0, n, (-1)^(n-i)*binomial(n,i)*(1 + 'y)^(i*(i-1))), n*(n-1)+1)}
{ for(n=1, 6, print(row(n))) } \\ Andrew Howroyd, Jan 28 2022
A121252
Number of labeled digraphs without isolated vertices and with n arcs.
Original entry on oeis.org
1, 2, 25, 520, 15150, 567540, 25986334, 1406214816, 87803248260, 6213408758960, 491423381371208, 42958461746823376, 4112928296979824348, 428022362222941505760, 48106759414197240877200, 5807382441785322296139392
Offset: 0
-
seq(value(Sum(binomial(m*(m-1),n)/2^(m+1),m=0..infinity)),n=0..20); # Vladeta Jovovic, Aug 25 2006
A217580
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.
Original entry on oeis.org
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
Offset: 0
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;
-
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
Showing 1-3 of 3 results.
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