%I #23 Mar 06 2022 08:38:16
%S 1,1,2,3,12,10,30,105,56,252,1260,330,1980,2574,2002,15015,240240,
%T 61880,15912,151164,38760,406980,4476780,1144066,13728792,24515700,
%U 6249100,84362850,21474180,5462730,81940950,1270084725,645122400
%N a(n) = lcm{1, ..., 2n} / binomial(2n, n).
%C Known to be always an integer.
%H Hojoo Lee, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;2e3bb004.0202">Re: LCM [1,2,..,N] > 2^{N-1}</a>, NMBRTHRY Mailing List, Feb 18 2002.
%H Daniel Ropp, <a href="https://cms.math.ca/publications/crux/issue?volume=13&issue=10">Solution to Problem 31</a>, Crux Mathematicorum, Vol. 13, No. 10 (1987), p. 314.
%F a(n) = A099996(n) / A000984(n) = A003418(2*n) / A001405(2*n) = A180000(2*n) = A263673(2*n).
%F a(n) = n * A068553(n) = n * A048619(2*n-1).
%t a[0] = 1; a[n_] := (LCM @@ Range[2*n])/Binomial[2*n, n]; Array[a, 33, 0] (* _Amiram Eldar_, Mar 06 2022 *)
%o (PARI) a(n) = lcm([1..2*n])/binomial(2*n, n); \\ _Michel Marcus_, Mar 06 2022
%Y Bisection of A180000 and A263673.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Mar 23 2002
%E a(0)=1 prepended by _Max Alekseyev_, Oct 23 2015