A156106 - OEIS

%I #15 Nov 30 2022 10:02:33

%S 1,3,15,99,783,6987,67671,694035,7418943,81800091,923720679,

%T 10630297827,124224709455,1470172954347,17585028636279,

%U 212248303720371,2581823992868703

%N Expansion of F(1/3,2/3;1/2;27*x/2) / F(1/3,-1/3;-1/2;27*x/2).

%C Hankel transform is 3^n*2^(n^2)*A005156 = 6^n*4^C(n,2)*A005156 = 3^n*A002416*A005156.

%H I. Gessel and G. Xin, <a href="https://arxiv.org/abs/math/0505217">The Generating Function of Ternary Trees and Continued Fractions</a>, arXiv:math/0505217 [math.CO], 2005.

%F D-finite with recurrence: 2*(2*n-1)*(n-2)*a(n) + (-72*(n-3)^2-171*n+420)*a(n-1) + (297*(n-3)^2+675*n-1674)*a(n-2) - 81*(3*n-5)*(3*n-7)*a(n-3) = 0. - _Georg Fischer_, Nov 30 2022

%K easy,nonn

%O 0,2

%A _Paul Barry_, Feb 04 2009