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

0,4

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.

Links

Table of n, a(n) for n=0..65.

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).

Example

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

Crossrefs

Sequence in context: A231206 A165241 A119865 * A193920 A076732 A130152

Adjacent sequences: A177893 A177894 A177895 * A177897 A177898 A177899

Keyword

nonn,tabl

Author

Paul Barry, Dec 15 2010

Status

approved