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%I #12 Apr 08 2013 03:47:23
%S 1,1,1,13,2,1,469,39,3,1,63577,1876,78,4,1,33231721,317885,4690,130,5,
%T 1,68519123173,199390326,953655,9380,195,6,1,562469619451069,
%U 479633862211,697866141,2225195,16415,273,7,1,18442242396353040817,4499756955608552,1918535448844,1860976376,4450390,26264,364,8,1
%N 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.
%C Row sums = 2^(n^2). First column (k = 0) is A173403.
%C Sum_{k=1,2,...,n} T(n,k)*k = A197927.
%F E.g.f.: exp(y*x)*A(x) where A(x) is the e.g.f. for A173403.
%e 1,
%e 1, 1,
%e 13, 2, 1,
%e 469, 39, 3, 1,
%e 63577, 1876, 78, 4, 1,
%e 33231721, 317885, 4690, 130, 5, 1,
%e 68519123173, 199390326, 953655, 9380, 195, 6, 1
%t 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
%K nonn,tabl
%O 0,4
%A _Geoffrey Critzer_, Oct 02 2012
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