A025540 Least common multiple of {C(0,0), C(2,1), ..., C(2n,n)}.

1, 2, 6, 60, 420, 1260, 13860, 360360, 360360, 6126120, 116396280, 116396280, 2677114440, 13385572200, 40156716600, 2329089562800, 72201776446800, 72201776446800, 72201776446800, 2671465728531600, 2671465728531600

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Mathoverflow, Asymptotic of LCM(binomial(2k,k)), 1<=k<=n

Crossrefs

Cf. A000984.

Programs

Mathematica

Table[LCM@@Table[Binomial[2n,n],{n,0,i}],{i,0,30}] (* Harvey P. Dale, Jun 04 2012 *)

PARI

a(n) = lcm(vector(n, k, binomial(2*k, k))); \\ Michel Marcus, Apr 13 2016

Formula

a(n) = 2^floor(log(n+1)/log(2)) * Prod( p^floor(log(2n)/log(p)) ), where the product is taken over all odd primes p below 2n. - Max Alekseyev, Apr 13 2016

If n = 2^k - 1, then a(n) = A099996(n) = A003418(2*n); otherwise a(n) = A099996(n)/2 = A003418(2*n)/2. - Max Alekseyev, Apr 13 2016