A025540 - OEIS

%I #25 Apr 13 2016 04:17:17

%S 1,2,6,60,420,1260,13860,360360,360360,6126120,116396280,116396280,

%T 2677114440,13385572200,40156716600,2329089562800,72201776446800,

%U 72201776446800,72201776446800,2671465728531600,2671465728531600

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

%H Vincenzo Librandi, <a href="/A025540/b025540.txt">Table of n, a(n) for n = 0..1000</a>

%H Mathoverflow, <a href="http://mathoverflow.net/q/236052">Asymptotic of LCM(binomial(2k,k)), 1<=k<=n</a>

%F 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

%F 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

%t Table[LCM@@Table[Binomial[2n,n],{n,0,i}],{i,0,30}] (* _Harvey P. Dale_, Jun 04 2012 *)

%o (PARI) a(n) = lcm(vector(n, k, binomial(2*k, k))); \\ _Michel Marcus_, Apr 13 2016

%Y Cf. A000984.

%K nonn

%O 0,2

%A _Clark Kimberling_