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A198261
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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.
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1
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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, 15, 0, 1, 1887284, 192143, 16128, 1435, 140, 21, 0, 1, 252522481, 15098272, 768572, 43008, 2870, 224, 28, 0, 1
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OFFSET
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0,7
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COMMENTS
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Row sums = 2^binomial(n,2) = A006125(n).
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LINKS
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FORMULA
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E.g.f. for column k: x^k/k! *A(x)/exp(x) where A(x) is the e.g.f. for A006125.
T(n,n) = 1 (the empty graph). - Geoffrey Critzer, Nov 11 2011
T(n,n-1) = 0. - Geoffrey Critzer, Nov 11 2011
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EXAMPLE
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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, 15, 0, 1;
1887284, 192143, 16128, 1435, 140, 21, 0, 1;
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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