This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A002474 #35 Jan 05 2025 09:40:20
%S A002474 2,16,384,18432,1474560,176947200,29727129600,6658877030400,
%T A002474 1917756584755200,690392370511872000,303772643025223680000,
%U A002474 160391955517318103040000,100084580242806496296960000,72861574416763129304186880000,61203722510081028615516979200000
%N A002474 Denominators of coefficients of odd powers of x of the expansion of Bessel function J_1(x).
%C A002474 The corresponding numerators are A033999(n) = (-1)^n.
%D A002474 Bronstein-Semendjajew, Taschenbuch der Mathematik, 7th German ed. 1965, ch. 4.4.7
%D A002474 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapters 49 and 52, equations 49:6:2 and 52:6:3 at page 483, 513.
%H A002474 T. D. Noe, <a href="/A002474/b002474.txt">Table of n, a(n) for n = 0..50</a>
%H A002474 <a href="/index/Di#divseq">Index to divisibility sequences</a>.
%H A002474 <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>.
%F A002474 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.
%F A002474 a(n) = 2^(2n+1)*A010790(n).
%e A002474 a(3) = 18432 = 128*6*24, since J_{1}(x) = x/2 - x^3/16 + x^5/384 - x^7/18432 + ...
%p A002474 a:= n-> denom(coeff(series(BesselJ(1, x), x, 2*n+2), x, 2*n+1)):
%p A002474 seq(a(n), n=0..15); # _Alois P. Heinz_, Sep 21 2024
%t A002474 CoefficientList[Series[BesselJ[1,x], {x,0,30}], x][[2 ;; ;; 2]]//Denominator
%t A002474 Table[2^(2*n+1)*n!*(n+1)!, {n,0,30}] (* _G. C. Greubel_, Sep 21 2024 *)
%o A002474 (PARI) a(n) = n!^2 * (n+1) << (2*n+1) \\ _Charles R Greathouse IV_, Oct 23 2023
%o A002474 (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
%o A002474 (Magma) [2^(2*n+1)*Factorial(n)*Factorial(n+1): n in [0..30]]; // _G. C. Greubel_, Sep 21 2024
%o A002474 (SageMath) [2^(2*n+1)*factorial(n)*factorial(n+1) for n in range(31)] # _G. C. Greubel_, Sep 21 2024
%Y A002474 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 A002474 Cf. A010790, A033999.
%K A002474 nonn,easy
%O A002474 0,1
%A A002474 _N. J. A. Sloane_
%E A002474 Name specified, numerators given, formula augmented by _Wolfdieter Lang_, Aug 25 2015