A068110 Denominators of coefficients in J0(i*sqrt(x))^2 power series where J0 denotes the ordinary Bessel function of order 0.

1, 2, 32, 576, 73728, 409600, 176947200, 17340825600, 1183800360960, 1725980926279680, 3451961852559360000, 39779750872350720000, 137478819014844088320000, 1858713633080692074086400, 377800756235068077873561600, 2550155104586709525646540800000, 20890870616774324434096462233600000

Offset: 0

Author

Benoit Cloitre, Mar 21 2002

Keywords

• easy
• frac
• nonn

References

• Bruce C. Berndt, Ramanujan's Notebooks, Part II, Springer-Verlag, 1989; see Hypergeometric series, p. 59.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..230

Crossrefs

Cf. A068111 (numerators).

Programs

Mathematica

Denominator[CoefficientList[Series[BesselJ[0, I*Sqrt[x]]^2, {x, 0, 15}], x]] (* Amiram Eldar, Jan 17 2025 *)

Formula

J0(i*sqrt(x))^2 = Sum_{n>=0} (2n)!/(n!)^4/2^(2n)*x^n.

Extensions

More terms from Amiram Eldar, Jan 17 2025