cp's OEIS Frontend

A100400 Triangle read by rows: T(n,k) is the number of nonroot nodes of outdegree k (0<=k<=n-1) in all non-crossing trees with n edges.

%I A100400 #7 Jan 14 2020 03:24:40
%S A100400 1,4,2,21,12,3,120,72,24,4,715,440,165,40,5,4368,2730,1092,312,60,6,
%T A100400 27132,17136,7140,2240,525,84,7,170544,108528,46512,15504,4080,816,
%U A100400 112,8,1081575,692208,302841,105336,29925,6840,1197,144,9,6906900,4440150,1973400,708400,212520,53130,10780,1680,180,10
%N A100400 Triangle read by rows: T(n,k) is the number of nonroot nodes of outdegree k (0<=k<=n-1) in all non-crossing trees with n edges.
%C A100400 Row n contains n terms. Row sums yield A004319. Column 0 yields A045721.
%H A100400 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 A100400 T(n, k) = (k+1)binomial(3n-k-2, 2n-1) (0<=k<=n-1).
%e A100400 T(2,1)=2 because in the non-crossing trees /_, _\ and /\ we have 2 nonroot nodes of outdegree 1.
%e A100400 Triangle begins:
%e A100400 1;
%e A100400 4,2;
%e A100400 21,12,3;
%e A100400 120,72,24,4;
%p A100400 for n from 1 to 10 do seq((k+1)*binomial(3*n-k-2,2*n-1),k=0..n-1) od; # yields sequence in triangular form
%Y A100400 Cf. A001764, A004319, A045721.
%K A100400 nonn,tabl
%O A100400 1,2
%A A100400 _Emeric Deutsch_, Dec 30 2004