%I A094040
%S A094040 1,1,1,1,3,3,1,6,14,12,1,10,40,75,55,1,15,90,275,429,273,1,21,175,770,
%T A094040 1911,2548,1428,1,28,308,1820,6370,13328,15504,7752,1,36,504,3822,17640,
%U A094040 51408,93024,95931,43263,1,45,780,7350,42840,162792,406980,648945
%N A094040 Triangle read by rows: T(n,k) is the number of noncrossing forests with 
               n vertices and k edges.
%C A094040 T(n,n-1) yields A001764; T(n,n-2) yields A026004.
%D A094040 P. Flajolet and M. Noy, Analytic combinatorics of noncrossing configurations, 
               Discrete Math. 204 (1999), 203-229.
%F A094040 T(n, k)=binomial(n, k+1)*binomial(n+2k-1, k)/(n+k) (0<=k<=n-1).
%e A094040 1; 1,1; 1,3,3; 1,6,14,12; 1,10,40,75,55; 1,15,90,275,429,273;
%e A094040 T(3,1)=3 because the noncrossing forests on 3 vertices A,B,C and having 
               one edge are (A, BC), (B, CA) and (C, AB).
%p A094040 T:=proc(n,k) if k<=n-1 then binomial(n,k+1)*binomial(n+2*k-1,k)/(n+k) 
               else 0 fi end: seq(seq(T(n,k),k=0..n-1),n=1..11);
%Y A094040 Cf. A001764, A026004.
%Y A094040 Sequence in context: A082009 A110640 A143389 this_sequence A039798 A001498 
               A138464
%Y A094040 Adjacent sequences: A094037 A094038 A094039 this_sequence A094041 A094042 
               A094043
%K A094040 nonn,tabl
%O A094040 1,5
%A A094040 Emeric Deutsch (deutsch(AT)duke.poly.edu), May 31 2004