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A072248 Triangle T(n,k) (n >= 2, 1 <= k <= n-1) giving number of non-crossing trees with n nodes and height k.

%I A072248 #18 Aug 12 2017 06:38:17
%S A072248 1,1,2,1,7,4,1,20,26,8,1,54,126,76,16,1,143,548,504,200,32,1,376,2259,
%T A072248 2900,1656,496,64,1,986,9034,15506,11528,4896,1184,128,1,2583,35469,
%U A072248 79354,73172,39552,13536,2752,256,1,6764,137644,394642,439272,285992,123904,35712,6272,512
%N A072248 Triangle T(n,k) (n >= 2, 1 <= k <= n-1) giving number of non-crossing trees with n nodes and height k.
%C A072248 For n >= 2, the n-th row has n-1 terms.
%H A072248 E. Deutsch and M. Noy, <a href="http://dx.doi.org/10.1016/S0012-365X(01)00366-1">Statistics on non-crossing trees</a>, Discrete Math., 254 (2002), 75-87.
%F A072248 Column g.f. are T(k) - T(k-1) (k = 1, 2, ...), where T(0) = z and T(k) = z/(1 - T(k-1)^2/z). - _Emeric Deutsch_, Dec 30 2004
%e A072248 Triangle T(n,k) begins:
%e A072248 1;
%e A072248 1,   2;
%e A072248 1,   7,    4;
%e A072248 1,  20,   26,     8;
%e A072248 1,  54,  126,    76,    16;
%e A072248 1, 143,  548,   504,   200,   32;
%e A072248 1, 376, 2259,  2900,  1656,  496,   64;
%e A072248 1, 986, 9034, 15506, 11528, 4896, 1184, 128;
%p A072248 T[0]:=z: for k from 1 to 10 do T[k]:=simplify(z/(1-T[k-1]^2/z)) od:for k from 1 to 10 do t[k]:=series(T[k]-T[k-1],z=0,15) od: for n from 2 to 11 do seq(coeff(t[k],z^n),k=1..n-1) od; # _Emeric Deutsch_, Dec 30 2004
%Y A072248 Cf. A001764, A072247.
%Y A072248 Row sums give A001764.
%K A072248 nonn,tabl
%O A072248 2,3
%A A072248 _N. J. A. Sloane_, Jul 06 2002
%E A072248 More terms from _Emeric Deutsch_, Dec 30 2004