A274656 Denominators of coefficients of z^n for the expansion of Fricke's hypergeometric function F_1(1/2,1/2;z).

1, 2, 64, 768, 98304, 655360, 10485760, 293601280, 30064771072, 1082331758592, 86586540687360, 60473139527680, 34832528367943680, 362258295026614272, 644014746713980928, 2576058986855923712, 5275768805080931762176, 32613843522318487257088

Offset: 0

Author

Wolfdieter Lang, Jul 07 2016

Keywords

• nonn
• easy
• frac

Comments

For the numerators see A274655.

For the denominators of the coefficients of z^n/n! for the expansion of F_1(1/2,1/2;z) see A274654.

See the main entry A274653 (with A274654) for the definition of Fricke's hypergeometric function F_1(a,b;z) with the recurrence and details on F_1(1/2,1/2;z).

Examples

			See A274653, A274654, A274655.
		

References

• See A274653.

Crossrefs

Cf. A274653.

Formula

a(n) = denominator(R(n)), where the rationals (in lowest terms) are R(n) = [z^n]F_1(1/2,1/2;z), and the recurrence for R(n) = r(n)/n! is obtained from the one given for r(n) in A274653.

R(n) = ((2*n-1)/(2*n))^2*R(n-1) + 2*C(n)/(n*(2*n-1)), n >= 1, R(0) = 0, with C(n) = ((2*n)!)^2 / (n!^4*2^(4*n)).