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A177896
A binomial conjugate of the Narayana numbers
0
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.
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
KEYWORD
nonn,tabl
AUTHOR
Paul Barry, Dec 15 2010
STATUS
approved