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 A123534 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). 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 REFERENCES R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977. LINKS Andrew Howroyd, Rows 3 through 20, flattened (first 15 rows from R. W. Robinson) EXAMPLE 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;   ... MATHEMATICA 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]]; Table[row[n], {n, 3, 15}] // Flatten (* Jean-François Alcover, Aug 13 2019, after Andrew Howroyd *) PROG (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)} { for(n=3, 7, print(row(n))) } \\ Andrew Howroyd, Nov 30 2018 CROSSREFS Row sums give A013922. Cf. A062734, A123527, A322139. Sequence in context: A120229 A266151 A192100 * A100960 A130852 A228335 Adjacent sequences:  A123531 A123532 A123533 * A123535 A123536 A123537 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Nov 13 2006 STATUS approved

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Last modified August 7 17:44 EDT 2020. Contains 336278 sequences. (Running on oeis4.)