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%I #11 Mar 30 2012 17:23:10
%S 1,0,1,1,0,1,4,3,0,1,41,16,6,0,1,768,205,40,10,0,1,27449,4608,615,80,
%T 15,0,1,1887284,192143,16128,1435,140,21,0,1,252522481,15098272,
%U 768572,43008,2870,224,28,0,1
%N Triangular array read by rows T(n,k) is the number of simple labeled graphs on n nodes with exactly k isolated nodes, 0<=k<=n.
%C Row sums = 2^binomial(n,2) = A006125(n).
%C First column (k=0) is A006129.
%F E.g.f. for column k: x^k/k! *A(x)/exp(x) where A(x) is the e.g.f. for A006125.
%F T(n,n) = 1 (the empty graph). - Geoffrey Critzer, Nov 11 2011
%F T(n,n-1) = 0. - Geoffrey Critzer, Nov 11 2011
%e 1;
%e 0, 1;
%e 1, 0, 1;
%e 4, 3, 0, 1;
%e 41, 16, 6, 0, 1;
%e 768, 205, 40, 10, 0, 1;
%e 27449, 4608, 615, 80, 15, 0, 1;
%e 1887284, 192143, 16128, 1435, 140, 21, 0, 1;
%t g=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, 20}]; Transpose[Table[Range[0, 10]! CoefficientList[Series[(x^n/n!)( g/Exp[x]), {x, 0, 10}], x], {n, 0, 8}]]//Grid
%K nonn,tabl
%O 0,7
%A _Geoffrey Critzer_, Oct 22 2011
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