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A177896 A binomial conjugate of the Narayana numbers.

%I A177896 #13 Jul 22 2025 08:10:12
%S A177896 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,
%T A177896 120,21,1,127,623,1246,1295,735,217,28,1,323,1800,4200,5292,3864,1624,
%U A177896 364,36,1,835,5211,13896,20580,18396,10080,3276,576,45,1,2188,15115,45345,77190,81690,55314,23730,6150,870,55,1
%N A177896 A binomial conjugate of the Narayana numbers.
%C A177896 Equals P^{-1}*N*P where P is A007318 and N is A001263.
%C A177896 First column is Motzkin numbers A001006. Row sums are A071356.
%C A177896 Diagonal sums are A078481.
%F A177896 G.f.: ( 1-x(1+y)-sqrt(1-2x(1+y)+x^2(1+y)(y-3)) )/(2x^2(1+y));
%F A177896 G.f.: 1/(1-x-xy-x^2(1+y)/(1-x-xy-x^2(1+y)/(1-... (continued fraction).
%e A177896 Triangle begins
%e A177896 1,
%e A177896 1, 1,
%e A177896 2, 3, 1,
%e A177896 4, 9, 6, 1,
%e A177896 9, 26, 26, 10, 1,
%e A177896 21, 75, 100, 60, 15, 1,
%e A177896 51, 216, 360, 295, 120, 21, 1,
%e A177896 127, 623, 1246, 1295, 735, 217, 28, 1,
%e A177896 323, 1800, 4200, 5292, 3864, 1624, 364, 36, 1
%K A177896 nonn,tabl
%O A177896 0,4
%A A177896 _Paul Barry_, Dec 15 2010