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A002474 Denominators of coefficients of odd powers of x of the expansion of Bessel function J_1(x). 13

%I

%S 2,16,384,18432,1474560,176947200,29727129600,6658877030400,

%T 1917756584755200,690392370511872000,303772643025223680000,

%U 160391955517318103040000,100084580242806496296960000

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

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

%D Bronstein-Semendjajew, Taschenbuch der Mathematik, 7th german ed. 1965, ch. 4.4.7

%H T. D. Noe, <a href="/A002474/b002474.txt">Table of n, a(n) for n = 0..50</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>

%F 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.

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

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

%Y 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

%Y Equals 2^(2n+1) A010790.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.

%E Name specified, numerators given, formula augmented. - _Wolfdieter Lang_, Aug 25 2015

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Last modified March 20 19:23 EDT 2019. Contains 321349 sequences. (Running on oeis4.)