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
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, since J_{1}(x) = x/2 - x^3/16 + x^5/384 - x^7/18432 + ...
MAPLE
a:= n-> denom(coeff(series(BesselJ(1, x), x, 2*n+2), x, 2*n+1)):
seq(a(n), n=0..15); # Alois P. Heinz, Sep 21 2024
MATHEMATICA
CoefficientList[Series[BesselJ[1, x], {x, 0, 30}], x][[2 ;; ;; 2]]//Denominator
Table[2^(2*n+1)*n!*(n+1)!, {n, 0, 30}] (* G. C. Greubel, Sep 21 2024 *)
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
(Magma) [2^(2*n+1)*Factorial(n)*Factorial(n+1): n in [0..30]]; // G. C. Greubel, Sep 21 2024
(SageMath) [2^(2*n+1)*factorial(n)*factorial(n+1) for n in range(31)] # G. C. Greubel, Sep 21 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Name specified, numerators given, formula augmented by Wolfdieter Lang, Aug 25 2015
STATUS
approved