Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Jan 04 2021 18:21:37
%S 1,0,0,0,3,0,0,10,10,0,0,15,340,15,0,0,21,6965,6965,21,0,0,28,51296,
%T 246295,51296,28,0,0,36,326676,14750946,14750946,326676,36,0,0,45,
%U 1917840,322476210,796058676,322476210,1917840,45,0,0,55,10683255
%N Triangle read by rows: T(n,k) = number of labeled bicolored nonseparable graphs with k points in one color class and n-k points in the other class. The classes are interchangeable if k = n-k. Here n >= 2, k=1..n-1.
%D R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.
%H Andrew Howroyd, <a href="/A123474/b123474.txt">Table of n, a(n) for n = 2..1276</a> (first 50 rows; first 24 rows from R. W. Robinson)
%H F. Harary and R. W. Robinson, <a href="http://dx.doi.org/10.4153/CJM-1979-007-3">Labeled bipartite blocks</a>, Canad. J. Math., 31 (1979), 60-68.
%F From _Andrew Howroyd_, Jan 03 2021: (Start)
%F T(n,k) = f(n-2*k) * binomial(n,k) * A123301(n, k) where f(0) = 1/2 and 1 otherwise.
%F A004100(n) = Sum_{k=0..floor(n/2)} T(n,k). (End)
%e Triangle begins:
%e 1;
%e 0, 0;
%e 0, 3, 0;
%e 0, 10, 10, 0;
%e 0, 15, 340, 15, 0;
%e 0, 21, 6965, 6965, 21, 0;
%e 0, 28, 51296, 246295, 51296, 28, 0;
%e ...
%e Formatted as an array:
%e ==========================================================
%e m/n | 1 2 3 4 5 6
%e ----+-----------------------------------------------------
%e 1 | 1 0 0 0 0 0 ...
%e 2 | 0 3 10 15 21 28 ...
%e 3 | 0 10 340 6965 51296 326676 ...
%e 4 | 0 15 6965 246295 14750946 322476210 ...
%e 5 | 0 21 51296 14750946 796058676 105725374062 ...
%e 6 | 0 28 326676 322476210 105725374062 9736032295374 ...
%e ...
%Y Central coefficients are A005335.
%Y Cf. A004100, A123301, A262307.
%K nonn,tabl
%O 2,5
%A _N. J. A. Sloane_, Nov 12 2006