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A189898
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Triangular array read by rows. T(n,k) is the number of digraphs with n labeled nodes having exactly k undirected (or weak) components, n >= 1, 1 <= k <= n.
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4
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1, 3, 1, 54, 9, 1, 3834, 243, 18, 1, 1027080, 20790, 675, 30, 1, 1067308488, 6364170, 67635, 1485, 45, 1, 4390480193904, 7543111716, 23031540, 171045, 2835, 63, 1, 72022346388181584, 35217115838604, 30469951764, 63580545, 370440, 4914, 84, 1
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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E.g.f. for column k: log(A(x))^k/k! where A(x) is the e.g.f. for A053763.
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EXAMPLE
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1
3 1
54 9 1
3834 243 18 1
1027080 20790 675 30 1
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MAPLE
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T:= (n, k)-> coeff(series(log(add(2^(i^2-i) *x^i/i!, i=0..n))^k /k!,
x, n+1), x, n) *n!:
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MATHEMATICA
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a= Sum[4^Binomial[n, 2]x^n/n!, {n, 0, 10}];
Transpose[Map[Drop[#, 1] &, Table[Range[0, 10]! CoefficientList[Series[Log[a]^n/n!, {x, 0, 10}], x], {n, 1, 10}]]] // Grid
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PROG
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# Adds a column 1, 0, 0, 0, ... at the left side of the triangle.
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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