This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A162717 #4 Jul 22 2025 06:56:25
%S A162717 1,1,1,1,2,1,1,3,4,1,1,4,10,7,1,1,5,20,27,11,1,1,6,35,77,61,16,1,1,7,
%T A162717 56,182,236,121,22,1,1,8,84,378,726,611,218,29,1,1,9,120,714,1902,
%U A162717 2375,1394,365,37,1,1,10,165,1254,4422,7667,6686,2885,577,46,1
%N A162717 A partial-sum Narayana product.
%C A162717 Row sums are A014137 (partial sums of Catalan numbers).
%C A162717 Equal to product of Riordan array (1/(1-x),x) and Narayana triangle A090181.
%F A162717 Number triangle T(n,k)=sum{j=0..n, C(n,j)*if(k<=j, C(j-1,2j-2k)*A000108(j-k),0)}; G.f.: 1/(1-x-x(1-x)y/(1-x/(1-xy/(1-x/(1-xy/(1-... (continued fraction).
%e A162717 Triangle begins
%e A162717 1,
%e A162717 1, 1,
%e A162717 1, 2, 1,
%e A162717 1, 3, 4, 1,
%e A162717 1, 4, 10, 7, 1,
%e A162717 1, 5, 20, 27, 11, 1,
%e A162717 1, 6, 35, 77, 61, 16, 1,
%e A162717 1, 7, 56, 182, 236, 121, 22, 1,
%e A162717 1, 8, 84, 378, 726, 611, 218, 29, 1,
%e A162717 1, 9, 120, 714, 1902, 2375, 1394, 365, 37, 1
%Y A162717 Cf. A104711.
%K A162717 easy,nonn,tabl
%O A162717 0,5
%A A162717 _Paul Barry_, Jul 11 2009