cp's OEIS Frontend

A068553 a(n) = lcm(1,2,...,2*n) / (n*binomial(2*n, n)).

%I A068553 #22 May 04 2023 03:29:23
%S A068553 1,1,1,3,2,5,15,7,28,126,30,165,198,143,1001,15015,3640,884,7956,1938,
%T A068553 19380,203490,49742,572033,980628,240350,3124550,766935,188370,
%U A068553 2731365,40970475,20160075,4962480,81880920,20173560,353037300
%N A068553 a(n) = lcm(1,2,...,2*n) / (n*binomial(2*n, n)).
%C A068553 Known to be always an integer.
%H A068553 Robert Israel, <a href="/A068553/b068553.txt">Table of n, a(n) for n = 1..3774</a>
%H A068553 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 A068553 a(n) = A068550(n)/n.
%F A068553 a(n) = A048619(2*n-1).
%p A068553 Num:= 2: Den:=2: Res:= 1:
%p A068553 for n from 2 to 100 do
%p A068553   Num:= ilcm(Num,2*n-1,2*n);
%p A068553   Den:= Den*(4+2/(n-1));
%p A068553   Res:= Res, Num/Den;
%p A068553 od:
%p A068553 Res; # _Robert Israel_, Dec 26 2018
%t A068553 Table[(LCM@@Range[2n])/(n Binomial[2n,n]),{n,40}] (* _Harvey P. Dale_, Jul 17 2012 *)
%o A068553 (Magma) [Lcm([1..2*n])/(n*(n+1)*Catalan(n)): n in [1..50]]; // _G. C. Greubel_, May 04 2023
%o A068553 (SageMath)
%o A068553 def A068553(n) -> int:
%o A068553     return lcm(range(1,2*n+1))//(n*binomial(2*n,n))
%o A068553 [A068553(n) for n in range(1,51)] # _G. C. Greubel_, May 04 2023
%Y A068553 Bisection of A048619.
%Y A068553 Cf. A068550.
%K A068553 nonn,easy
%O A068553 1,4
%A A068553 _N. J. A. Sloane_, Mar 23 2002