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

1, 1, 1, 3, 2, 5, 15, 7, 28, 126, 30, 165, 198, 143, 1001, 15015, 3640, 884, 7956, 1938, 19380, 203490, 49742, 572033, 980628, 240350, 3124550, 766935, 188370, 2731365, 40970475, 20160075, 4962480, 81880920, 20173560, 353037300

Offset: 1

Author

N. J. A. Sloane, Mar 23 2002

Keywords

• nonn
• easy

Comments

Known to be always an integer.

Links

• Robert Israel, Table of n, a(n) for n = 1..3774
• Hojoo Lee, Re: LCM [1,2,..,N] > 2^{N-1}, NMBRTHRY Mailing List, Feb 18 2002.

Crossrefs

Bisection of A048619.

Cf. A068550.

Programs

Magma

[Lcm([1..2*n])/(n*(n+1)*Catalan(n)): n in [1..50]]; // G. C. Greubel, May 04 2023

Maple

Num:= 2: Den:=2: Res:= 1:
for n from 2 to 100 do
  Num:= ilcm(Num,2*n-1,2*n);
  Den:= Den*(4+2/(n-1));
  Res:= Res, Num/Den;
od:
Res; # Robert Israel, Dec 26 2018

Mathematica

Table[(LCM@@Range[2n])/(n Binomial[2n,n]),{n,40}] (* Harvey P. Dale, Jul 17 2012 *)

SageMath

def A068553(n) -> int:
    return lcm(range(1,2*n+1))//(n*binomial(2*n,n))
[A068553(n) for n in range(1,51)] # G. C. Greubel, May 04 2023

Formula

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

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