%I A132813
%S A132813 1,1,2,1,6,3,1,12,18,4,1,20,60,40,5,1,30,150,200,75,6,1,42,315,700,525,
%T A132813 126,7,1,56,588,1960,2450,1176,196,8,1,72,1008,4704,8820,7056,2352,288,
%U A132813 9,1,90,1620,10080,26460,31752,17640,4320,405,10
%N A132813 Triangle read by rows: A001263 * A127648 as infinite lower triangular 
               matrices.
%C A132813 Row sums = A001700: (1, 3, 10, 35, 126,...).
%C A132813 Also a(n,k) = binomial[n - 1, k - 1]*binomial[n, k - 1], related to Narayana 
               polynomials (see Sulanke reference). - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), 
               Apr 09 2008
%D A132813 Sulanke, R. A. "Counting Lattice Paths by Narayana Polynomials." Electronic 
               J. Combinatorics 7, No. 1, R40, 1-9, 2000. http://www.combinatorics.org/
               Volume_7/Abstracts/v7i1r40.html.
%F A132813 T(n,k)= (k+1)*binomial(n+1,k+1)*binomial(n+1,k)/(n+1), n>=k>=0.
%e A132813 First few rows of the triangle are:
%e A132813 1;
%e A132813 1, 2;
%e A132813 1, 6, 3;
%e A132813 1, 12, 18, 4;
%e A132813 1, 20, 60, 40, 5;
%e A132813 1, 30, 150, 200, 75, 6;
%e A132813 1, 42, 315, 700, 525, 126, 7,
%e A132813 ...
%t A132813 A[n_,k_]=Binomial[n-1,k-1]*Binomial[n,k-1]; Table[Table[A[n,k],{k,1,n}],
               {n,1,11}]; Flatten[%] - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), 
               Apr 09 2008
%Y A132813 Cf. A127648, A001263, A001700.
%Y A132813 Sequence in context: A142977 A120108 A060556 this_sequence A034898 A059300 
               A046803
%Y A132813 Adjacent sequences: A132810 A132811 A132812 this_sequence A132814 A132815 
               A132816
%K A132813 nonn,tabl
%O A132813 0,3
%A A132813 Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2007