A162717 A partial-sum Narayana product.
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, 56, 182, 236, 121, 22, 1, 1, 8, 84, 378, 726, 611, 218, 29, 1, 1, 9, 120, 714, 1902, 2375, 1394, 365, 37, 1, 1, 10, 165, 1254, 4422, 7667, 6686, 2885, 577, 46, 1
Offset: 0
Examples
Triangle begins 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, 56, 182, 236, 121, 22, 1, 1, 8, 84, 378, 726, 611, 218, 29, 1, 1, 9, 120, 714, 1902, 2375, 1394, 365, 37, 1
Crossrefs
Cf. A104711.
Formula
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).
Comments