A068553 - OEIS

%I #22 May 04 2023 03:29:23

%S 1,1,1,3,2,5,15,7,28,126,30,165,198,143,1001,15015,3640,884,7956,1938,

%T 19380,203490,49742,572033,980628,240350,3124550,766935,188370,

%U 2731365,40970475,20160075,4962480,81880920,20173560,353037300

%N a(n) = lcm(1,2,...,2*n) / (n*binomial(2*n, n)).

%C Known to be always an integer.

%H Robert Israel, <a href="/A068553/b068553.txt">Table of n, a(n) for n = 1..3774</a>

%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.

%F a(n) = A068550(n)/n.

%F a(n) = A048619(2*n-1).

%p Num:= 2: Den:=2: Res:= 1:

%p for n from 2 to 100 do

%p   Num:= ilcm(Num,2*n-1,2*n);

%p   Den:= Den*(4+2/(n-1));

%p   Res:= Res, Num/Den;

%p od:

%p Res; # _Robert Israel_, Dec 26 2018

%t Table[(LCM@@Range[2n])/(n Binomial[2n,n]),{n,40}] (* _Harvey P. Dale_, Jul 17 2012 *)

%o (Magma) [Lcm([1..2*n])/(n*(n+1)*Catalan(n)): n in [1..50]]; // _G. C. Greubel_, May 04 2023

%o (SageMath)

%o def A068553(n) -> int:

%o     return lcm(range(1,2*n+1))//(n*binomial(2*n,n))

%o [A068553(n) for n in range(1,51)] # _G. C. Greubel_, May 04 2023

%Y Bisection of A048619.

%Y Cf. A068550.

%K nonn,easy

%O 1,4

%A _N. J. A. Sloane_, Mar 23 2002