A068111 Numerators of coefficients in J0(i*sqrt(x))^2, where J0 denotes the ordinary Bessel function of order 0.

1, 1, 3, 5, 35, 7, 77, 143, 143, 2431, 46189, 4199, 96577, 7429, 7429, 215441, 6678671, 392863, 392863, 765049, 765049, 31367009, 1348781387, 58642669, 2756205443, 2756205443, 2756205443, 146078888479, 146078888479, 5037203051, 297194980009, 584803025179, 584803025179

Offset: 0

Author

Benoit Cloitre, Mar 21 2002

Keywords

• easy
• frac
• nonn

Comments

The product of the odd primes between n+1 and 2n. inclusive. - T. D. Noe, Jan 24 2007

Examples

			Fractions begin with 1, 1/2, 3/32, 5/576, 35/73728, 7/409600, 77/176947200, 143/17340825600, 143/1183800360960, 2431/1725980926279680, 46189/3451961852559360000, 4199/39779750872350720000, ...
		

Links

• T. D. Noe, Table of n, a(n) for n=0..250

Crossrefs

Cf. A068110 (denominators).

Programs

Mathematica

Numerator[CoefficientList[Series[BesselJ[0, I*Sqrt[x]]^2, {x, 0, 30}], x]] (* Amiram Eldar, Jan 17 2025 *)

Formula

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