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%I #8 May 19 2020 12:58:30
%S 1,2,1,3,4,1,4,10,7,1,5,20,27,11,1,6,35,77,61,16,1,7,56,182,236,121,
%T 22,1,8,84,378,726,611,218,29,1,9,120,714,1902,2375,1394,365,37,1,10,
%U 165,1254,4422,7667,6686,2885,577,46,1,11,220,2079,9372,21527,26090,16745
%N Triangle T(n,m) = sum_{k=m..n} A001263(k,m).
%C This summation over columns of the Narayana triangle could also be defined as a multiplication
%C of the Narayana triangle from the left by the lower-left triangle represented by the all-1 sequence A000012.
%F Row sums: sum_{m=1..n} T(n,m) = A014138(n).
%e First few rows of the triangle are:
%e 1;
%e 2, 1;
%e 3, 4, 1;
%e 4, 10, 7, 1;
%e 5, 20, 27, 11, 1;
%e 6, 35, 77, 61, 16, 1;
%e ...
%o (Python)
%o from sympy import binomial
%o def A001263(n,m):
%o return binomial(n-1,m-1)*binomial(n,m-1)//m
%o def A104711(n,m):
%o a = 0
%o for k in range(m,n+1):
%o a += A001263(k,m)
%o return a
%o print([A104711(n,m) for n in range(20) for m in range(1,n+1)]) # _R. J. Mathar_, Oct 11 2009
%Y Cf. A014138, A104710, A005585, A000124.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Mar 19 2005
%E Extended by _R. J. Mathar_, Oct 11 2009
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