A162747 A factorial-Pascal matrix.
1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1, 1, 15, 50, 50, 15, 1, 1, 21, 105, 176, 105, 21, 1, 1, 28, 196, 497, 497, 196, 28, 1, 1, 36, 336, 1204, 1830, 1204, 336, 36, 1, 1, 45, 540, 2604, 5634, 5634, 2604, 540, 45, 1, 1, 55, 825, 5160, 15150, 21642, 15150, 5160, 825
Offset: 0
Examples
Triangle begins 1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1, 1, 15, 50, 50, 15, 1, 1, 21, 105, 176, 105, 21, 1, 1, 28, 196, 497, 497, 196, 28, 1, 1, 36, 336, 1204, 1830, 1204, 336, 36, 1, 1, 45, 540, 2604, 5634, 5634, 2604, 540, 45, 1, 1, 55, 825, 5160, 15150, 21642, 15150, 5160, 825, 55, 1
Formula
Number triangle T(n,k)=sum{j=0..n, C(n,j)*C(n-j,2(k-j))*if(j<=k,(k-j)!,0)}.
G.f.: 1/(1-x-xy-x^2*y/(1-x-xy-x^2*y/(1-x-xy-2x^2*y/(1-x-xy-2x^2*y/(1-x-xy-3x^2*y/(1-... (continued fraction). [From Paul Barry, Apr 12 2010]
Comments