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%I #12 Aug 13 2019 13:18:28
%S 1,3,6,1,12,70,100,45,10,1,60,720,2445,3535,2697,1335,455,105,15,1,
%T 360,7560,46830,133581,216951,232820,183540,111765,53627,20307,5985,
%U 1330,210,21,1,2520,84000,835800,3940440,10908688,20317528
%N 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).
%D R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.
%H Andrew Howroyd, <a href="/A123534/b123534.txt">Rows 3 through 20, flattened</a> (first 15 rows from R. W. Robinson)
%e Triangle begins (n >= 3, k >= n):
%e n
%e 3 | 1;
%e 4 | 3, 6, 1;
%e 5 | 12, 70, 100, 45, 10, 1;
%e 6 | 60, 720, 2445, 3535, 2697, 1335, 455, 105, 15, 1;
%e ...
%t 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]];
%t Table[row[n], {n, 3, 15}] // Flatten (* _Jean-François Alcover_, Aug 13 2019, after _Andrew Howroyd_ *)
%o (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)}
%o { for(n=3, 7, print(row(n))) } \\ _Andrew Howroyd_, Nov 30 2018
%Y Row sums give A013922.
%Y Cf. A062734, A123527, A322139.
%K nonn,tabf
%O 3,2
%A _N. J. A. Sloane_, Nov 13 2006
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