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A260040 Triangle read by rows giving numbers H(n,k), number of classes of twin-tree-rooted maps with n edges whose root bond contains k edges.

%I A260040 #19 Jul 23 2015 04:07:34
%S A260040 1,8,1,72,15,1,720,190,24,1,7780,2345,415,35,1,89040,29127,6384,798,
%T A260040 48,1,1064644,367248,93324,15162,1400,63,1,13173216,4708344,1332528,
%U A260040 261708,32400,2292,80,1,167522976,61343667,18829650,4271652,657198,63690,3555,99,1,2178520080,811147590,265116720,67358500,12269312,1506615,117040,5280,120,1
%N A260040 Triangle read by rows giving numbers H(n,k), number of classes of twin-tree-rooted maps with n edges whose root bond contains k edges.
%C A260040 See Mullin (1967) for precise definition.
%C A260040 The sequence 1, 8, 72, 720,... in the first column has the same values as in A260039.
%H A260040 R. C. Mullin, <a href="http://dx.doi.org/10.1016/S0021-9800(67)80001-2">On the average activity of a spanning tree of a rooted map</a>, J. Combin. Theory, 3 (1967), 103-121.
%H A260040 R. C. Mullin, <a href="/A260039/a260039.pdf">On the average activity of a spanning tree of a rooted map</a>, J. Combin. Theory, 3 (1967), 103-121. [Annotated scanned copy]
%F A260040 (k+1)*T(n,k) = A260039(n,k), n>=1, 0<=k<n. [Mullin Eq. (7.1)]
%F A260040 Conjecture: T(n,n-2) = A005563(n) = 8, 15, 24,.... for n>=2. - _R. J. Mathar_, Jul 22 2015
%F A260040 Conjecture: T(n,n-3)= (n+1)*n*(5*n^2+7*n+6)/12 = 72, 190,.... for n>=3. - _R. J. Mathar_, Jul 22 2015
%e A260040 Triangle begins:
%e A260040 1,
%e A260040 8,1,
%e A260040 72,15,1,
%e A260040 720,190,24,1,
%e A260040 ...
%Y A260040 Row sums are A260041.
%K A260040 nonn,tabl
%O A260040 1,2
%A A260040 _N. J. A. Sloane_, Jul 22 2015