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

0,3

Comments

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

Links

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

Formula

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

Example

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, ...

Mathematica

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

Crossrefs

Cf. A068110 (denominators).

Sequence in context: A222630 A187993 A221158 * A162444 A305858 A379507

Adjacent sequences: A068108 A068109 A068110 * A068112 A068113 A068114

Keyword

easy,frac,nonn

Author

Benoit Cloitre, Mar 21 2002

Status

approved