A217436 Triangular array read by rows. T(n,k) is the number of labeled relations on n elements with exactly k vertices of indegree and outdegree = 0.

1, 1, 1, 13, 2, 1, 469, 39, 3, 1, 63577, 1876, 78, 4, 1, 33231721, 317885, 4690, 130, 5, 1, 68519123173, 199390326, 953655, 9380, 195, 6, 1, 562469619451069, 479633862211, 697866141, 2225195, 16415, 273, 7, 1, 18442242396353040817, 4499756955608552, 1918535448844, 1860976376, 4450390, 26264, 364, 8, 1

Offset: 0

Author

Geoffrey Critzer, Oct 02 2012

Keywords

• nonn
• tabl

Comments

Row sums = 2^(n^2). First column (k = 0) is A173403.

Sum_{k=1,2,...,n} T(n,k)*k = A197927.

Examples

			1,
1, 1,
13, 2, 1,
469, 39, 3, 1,
63577, 1876, 78, 4, 1,
33231721, 317885, 4690, 130, 5, 1,
68519123173, 199390326, 953655, 9380, 195, 6, 1
		

Programs

Mathematica

nn=6; s=Sum[Sum[(-1)^k Binomial[n,k] 2^(n-k)^2, {k,0,n}] x^n/n!, {n,0,nn}]; Range[0,nn]! CoefficientList[Series[Exp[ y x] s, {x,0,nn}], {x,y}] //Grid

Formula

E.g.f.: exp(y*x)*A(x) where A(x) is the e.g.f. for A173403.