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A217563
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Irregular triangular array read by rows. T(n,k) is the number of weakly connected relations on n labeled nodes with k arcs. (n>=0, 0<=k<=n^2)
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0
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1, 1, 1, 0, 2, 5, 4, 1, 0, 0, 12, 56, 111, 123, 84, 36, 9, 1, 0, 0, 0, 128, 944, 3264, 7096, 10936, 12687, 11400, 8004, 4368, 1820, 560, 120, 16, 1, 0, 0, 0, 0, 2000, 21104, 109400, 373920, 950725, 1915405, 3168880, 4394760, 5169230, 5188390, 4454000
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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E.g.f.: Log[Sum_{n>=0} (1+y)^(n^2) x^n/n!] + 1
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EXAMPLE
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1,
1, 1,
0, 2, 5, 4, 1,
0, 0, 12, 56, 111, 123, 84, 36, 9, 1,
0, 0, 0, 128, 944, 3264, 7096, 10936, 12687, 11400, 8004, 4368, 1820, 560, 120, 16, 1
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MATHEMATICA
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nn=6; s=Sum[(1+y)^(n^2) x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[ Log[s]+1, {x, 0, nn}], {x, y}] //Grid
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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