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A123534
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Triangular array T(n,k) giving number of 2-connected graphs with n labeled nodes and k edges (n >= 3, n <= k <= n(n-1)/2).
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6
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1, 3, 6, 1, 12, 70, 100, 45, 10, 1, 60, 720, 2445, 3535, 2697, 1335, 455, 105, 15, 1, 360, 7560, 46830, 133581, 216951, 232820, 183540, 111765, 53627, 20307, 5985, 1330, 210, 21, 1, 2520, 84000, 835800, 3940440, 10908688, 20317528
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OFFSET
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3,2
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REFERENCES
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R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.
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LINKS
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EXAMPLE
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Triangle begins (n >= 3, k >= n):
n
3 | 1;
4 | 3, 6, 1;
5 | 12, 70, 100, 45, 10, 1;
6 | 60, 720, 2445, 3535, 2697, 1335, 455, 105, 15, 1;
...
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MATHEMATICA
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row[n_] := row[n] = Module[{s}, s = (n-1)!*Log[x/InverseSeries[#, x]& @ (x*D[#, x]& @ Log[Sum[(1+y)^Binomial[k, 2]*x^k/k!, {k, 0, n}] + O[x]^(n+1) ])]; CoefficientList[Coefficient[s, x, n-1]/y^n, y]];
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PROG
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(PARI) row(n)={Vecrev((n-1)!*polcoef(log(x/serreverse(x*deriv(log(sum(k=0, n, (1 + y)^binomial(k, 2) * x^k / k!) + O(x*x^n))))), n-1)/y^n)}
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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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