A068550 a(n) = lcm{1, ..., 2n} / binomial(2n, n).

1, 1, 2, 3, 12, 10, 30, 105, 56, 252, 1260, 330, 1980, 2574, 2002, 15015, 240240, 61880, 15912, 151164, 38760, 406980, 4476780, 1144066, 13728792, 24515700, 6249100, 84362850, 21474180, 5462730, 81940950, 1270084725, 645122400

Offset: 0

Author

N. J. A. Sloane, Mar 23 2002

Keywords

• nonn
• easy

Comments

Known to be always an integer.

Links

• Hojoo Lee, Re: LCM [1,2,..,N] > 2^{N-1}, NMBRTHRY Mailing List, Feb 18 2002.
• Daniel Ropp, Solution to Problem 31, Crux Mathematicorum, Vol. 13, No. 10 (1987), p. 314.

Crossrefs

Bisection of A180000 and A263673.

Programs

Mathematica

a[0] = 1; a[n_] := (LCM @@ Range[2*n])/Binomial[2*n, n]; Array[a, 33, 0] (* Amiram Eldar, Mar 06 2022 *)

PARI

a(n) = lcm([1..2*n])/binomial(2*n, n); \\ Michel Marcus, Mar 06 2022

Formula

a(n) = A099996(n) / A000984(n) = A003418(2*n) / A001405(2*n) = A180000(2*n) = A263673(2*n).

a(n) = n * A068553(n) = n * A048619(2*n-1).

Extensions

a(0)=1 prepended by Max Alekseyev, Oct 23 2015