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A062735
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Triangular array T(n,k) giving number of weakly connected digraphs with n labeled nodes and k arcs (n >= 1, 0 <= k <= n(n-1)).
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11
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1, 0, 2, 1, 0, 0, 12, 20, 15, 6, 1, 0, 0, 0, 128, 432, 768, 920, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 2000, 11104, 33880, 73480, 123485, 166860, 184426, 167900, 125965, 77520, 38760, 15504, 4845, 1140, 190, 20, 1, 0, 0, 0, 0, 0, 41472, 337920, 1536000, 5062080
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OFFSET
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1,3
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LINKS
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FORMULA
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E.g.f.: 1+log( Sum_{n >= 0, k >= 0} binomial(n*(n-1), k)*x^n/n!*y^k ).
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EXAMPLE
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1;
0, 2, 1;
0, 0, 12, 20, 15, 6, 1;
0, 0, 0, 128, 432, 768, 920, 792, 495, 220, 66, 12, 1;
0, 0, 0, 0, 2000, 11104, 33880, 73480, 123485, 166860, 184426, 167900, ...;
0, 0, 0, 0, 0, 41472, 337920,1536000,5062080,.. ;
0, 0, 0, 0, 0, 0, 1075648,...
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MATHEMATICA
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nn=7; s=Sum[(1+y)^(n^2-n) x^n/n!, {n, 0, nn}]; Range[0, nn]!CoefficientList[Series[Log[ s]+1, {x, 0, nn}], {x, y}]//Grid (* returns triangle indexed from n = 0, Geoffrey Critzer, Oct 07 2012 *)
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PROG
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(PARI) row(n)={Vecrev(n!*polcoef(1 + log(sum(k=0, n, (1+y)^(k*(k-1))*x^k/k!, O(x*x^n))), n))}
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CROSSREFS
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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STATUS
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approved
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