OFFSET
0,1
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=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
KEYWORD
nonn
AUTHOR
STATUS
approved