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A217653
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Triangular array read by rows: T(n,k) is the number of unlabeled simple graphs with n nodes that have exactly k isolated nodes, (n>=0, 0<=k<=n).
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1
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1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 7, 2, 1, 0, 1, 23, 7, 2, 1, 0, 1, 122, 23, 7, 2, 1, 0, 1, 888, 122, 23, 7, 2, 1, 0, 1, 11302, 888, 122, 23, 7, 2, 1, 0, 1, 262322, 11302, 888, 122, 23, 7, 2, 1, 0, 1, 11730500, 262322, 11302, 888, 122, 23, 7, 2, 1, 0, 1
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OFFSET
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0,7
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COMMENTS
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Sum_{k=1..n} T(n,k)*k = A006897(n).
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LINKS
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FORMULA
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O.g.f.: A(x)/(1-y*x) where A(x) is o.g.f. for A002494.
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EXAMPLE
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1,
0, 1,
1, 0, 1,
2, 1, 0, 1,
7, 2, 1, 0, 1,
23, 7, 2, 1, 0, 1,
122, 23, 7, 2, 1, 0, 1
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MATHEMATICA
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Needs["Combinatorica`"]; nn=10; s=Sum[NumberOfGraphs[n]x^n, {n, 0, nn}]; CoefficientList[Series[s (1-x)/(1-y x), {x, 0, nn}], {x, y}] //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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