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.

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

Author

Geoffrey Critzer, Oct 07 2012

Keywords

• nonn
• tabl

Comments

Column k=0 is A054545.

Examples

			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;
		

Programs

Mathematica

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

Formula

E.g.f.: exp(y*x)*A(x) where A(x) is the e.g.f. for A054545.