A162717 - OEIS

%I #2 Mar 30 2012 18:59:25

%S 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 56,182,236,121,22,1,1,8,84,378,726,611,218,29,1,1,9,120,714,1902,

%U 2375,1394,365,37,1,1,10,165,1254,4422,7667,6686,2885,577,46,1

%N A partial-sum Narayana product

%C Row sums are A014137 (partial sums of Catalan numbers).

%C Equal to product of Riordan array (1/(1-x),x) and Narayana triangle A090181.

%F 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 Triangle begins

%e 1,

%e 1, 1,

%e 1, 2, 1,

%e 1, 3, 4, 1,

%e 1, 4, 10, 7, 1,

%e 1, 5, 20, 27, 11, 1,

%e 1, 6, 35, 77, 61, 16, 1,

%e 1, 7, 56, 182, 236, 121, 22, 1,

%e 1, 8, 84, 378, 726, 611, 218, 29, 1,

%e 1, 9, 120, 714, 1902, 2375, 1394, 365, 37, 1

%Y Cf. A104711.

%K easy,nonn,tabl

%O 0,5

%A _Paul Barry_, Jul 11 2009