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A104711 Triangle T(n,m) = sum_{k=m..n} A001263(k,m).

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