A002506 Denominators of coefficients of expansion of Bessel function J_2(x).

8, 96, 3072, 184320, 17694720, 2477260800, 475634073600, 119859786547200, 38355131695104000, 15188632151261184000, 7290543432605368320000, 4170190843450270679040000, 2802368246798581896314880000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			a(2) = 3072 = 64*2*24, J2(x) = x^2/8 - x^4/96 + x^6/3072 - x^8/184320 +- ...
		

References

• Bronstein-Semendjajew, Taschenbuch der Mathematik, 7th German ed. 1965, ch. 4.4.7

Links

• T. D. Noe, Table of n, a(n) for n = 0..50
• Index entries for sequences related to Bessel functions or polynomials

Crossrefs

J0: A002454, J1: A002474, J3: A014401.

Programs

Mathematica

Denominator[Take[CoefficientList[Series[BesselJ[2,x],{x,0,30}],x],{3,-1,2}]] (* Harvey P. Dale, Sep 21 2013 *)

Formula

a(n) = 2^(2n+k) * n! * (n+k)! here for k=2, i.e., Bessel's J2(x).

a(n) - 4*n*(n+2)*a(n-1) = 0. - R. J. Mathar, Jun 20 2013

Extensions

Previous Mathematica program corrected by Harvey P. Dale, Sep 21 2013