A156106 Expansion of F(1/3,2/3;1/2;27*x/2) / F(1/3,-1/3;-1/2;27*x/2).

1, 3, 15, 99, 783, 6987, 67671, 694035, 7418943, 81800091, 923720679, 10630297827, 124224709455, 1470172954347, 17585028636279, 212248303720371, 2581823992868703

Offset: 0

Author

Paul Barry, Feb 04 2009

Keywords

• easy
• nonn

Comments

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

Links

• I. Gessel and G. Xin, The Generating Function of Ternary Trees and Continued Fractions, arXiv:math/0505217 [math.CO], 2005.

Formula

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