A002474 Denominators of coefficients of odd powers of x of the expansion of Bessel function J_1(x).

2, 16, 384, 18432, 1474560, 176947200, 29727129600, 6658877030400, 1917756584755200, 690392370511872000, 303772643025223680000, 160391955517318103040000, 100084580242806496296960000

Offset

0,1

Comments

The corresponding numerators are A033999(n) = (-1)^n.

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 to divisibility sequences

Index entries for sequences related to Bessel functions or polynomials

Formula

a(n) = 2^(2n+k) * n! * (n+k)! here for k=1, i.e., Bessel's J1(x) has the denominator a(n) for the coefficient of x^(2*n+1), n >= 0.

a(n) = 2^(2n+1)*A010790(n).

Example

a(3) = 18432 = 128*6*24, J1(x) = x/2 - x^3/16 + x^5/384 - x^7/18432 +- ...

Mathematica

Series[ BesselJ[ 1, x ], {x, 0, 30} ]

Prog

(PARI) a(n) = n!^2 * (n+1) << (2*n+1) \\ Charles R Greathouse IV, Oct 23 2023
(PARI) first(n)=my(x='x+O('x^(2*n+1)), t=besselj(1, x)); vector(n+1, k, 2*denominator(polcoeff(t, 2*k-2))) \\ Charles R Greathouse IV, Oct 23 2023

Crossrefs

Cf. J_0: A002454, J_2: A002506, J_3: A014401, J_4: A061403, J_5: A061404, J_6: A061405, J_7: A061407, J_9: A061440 J_10: A061441.

Cf. A010790, A033999.

Sequence in context: A140308 A280723 A052737 * A172149 A340563 A295710

Adjacent sequences: A002471 A002472 A002473 * A002475 A002476 A002477

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Name specified, numerators given, formula augmented by Wolfdieter Lang, Aug 25 2015

Status

approved