A177896 A binomial conjugate of the Narayana numbers.

1, 1, 1, 2, 3, 1, 4, 9, 6, 1, 9, 26, 26, 10, 1, 21, 75, 100, 60, 15, 1, 51, 216, 360, 295, 120, 21, 1, 127, 623, 1246, 1295, 735, 217, 28, 1, 323, 1800, 4200, 5292, 3864, 1624, 364, 36, 1, 835, 5211, 13896, 20580, 18396, 10080, 3276, 576, 45, 1, 2188, 15115, 45345, 77190, 81690, 55314, 23730, 6150, 870, 55, 1

Offset: 0

Author

Paul Barry, Dec 15 2010

Keywords

• nonn
• tabl

Comments

Equals P^{-1}*N*P where P is A007318 and N is A001263.

First column is Motzkin numbers A001006. Row sums are A071356.

Diagonal sums are A078481.

Examples

			Triangle begins
1,
1, 1,
2, 3, 1,
4, 9, 6, 1,
9, 26, 26, 10, 1,
21, 75, 100, 60, 15, 1,
51, 216, 360, 295, 120, 21, 1,
127, 623, 1246, 1295, 735, 217, 28, 1,
323, 1800, 4200, 5292, 3864, 1624, 364, 36, 1
		

Formula

G.f.: ( 1-x(1+y)-sqrt(1-2x(1+y)+x^2(1+y)(y-3)) )/(2x^2(1+y));

G.f.: 1/(1-x-xy-x^2(1+y)/(1-x-xy-x^2(1+y)/(1-... (continued fraction).