A014401 Denominators of coefficients of expansion of Bessel function J_3(x).

48, 768, 30720, 2211840, 247726080, 39636172800, 8561413324800, 2397195730944000, 843812897292288000, 364527171630268416000, 189554129247739576320000, 116765343616607579013120000

Offset

0,1

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

Formula

a(n) = 2^(2n+k) * n! * (n+k)! here for k=3, i.e., Bessel's J3(x).

D-finite with recurrence: a(n) - (4*n^2 + 4*n*k)*a(n-1) = 0, a(0) = 2^k*k!, here for k=3. - Georg Fischer, Mar 22 2022

Example

a(1) = 768 = 32*24, J3(x) = x^3/48 - x^5/768 + x^7/30720 - x^9/2211840 +- ...

Maple

k:=3: f:= gfun:-rectoproc({a(n)-(4*n^2 + 4*n*k)*a(n-1), a(0)=2^k*k!}, a(n), remember): map(f, [$0..16]); # Georg Fischer, Mar 22 2022

Mathematica

Denominator[Take[CoefficientList[Series[BesselJ[3, x], {x, 0, 30}], x], {4, -1, 2}]] (* Harvey P. Dale, Dec 10 2011 *)

Crossrefs

J0: A002454, J1: A002474, J2: A002506.

Sequence in context: A105948 A350378 A192839 * A241873 A233784 A233959

Adjacent sequences: A014398 A014399 A014400 * A014402 A014403 A014404

Keyword

nonn

Author

N. J. A. Sloane

Status

approved