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A263673 a(n) = lcm{1,2,...,n} / binomial(n,floor(n/2)).

%I A263673 #33 Mar 04 2018 09:38:29
%S A263673 1,1,1,2,2,6,3,12,12,20,10,60,30,210,105,56,56,504,252,2520,1260,660,
%T A263673 330,3960,1980,5148,2574,4004,2002,30030,15015,240240,240240,123760,
%U A263673 61880,31824,15912,302328,151164,77520,38760,813960,406980,8953560,4476780,2288132,1144066,27457584,13728792,49031400
%N A263673 a(n) = lcm{1,2,...,n} / binomial(n,floor(n/2)).
%C A263673 From _Robert Israel_, Oct 23 2015: (Start)
%C A263673 If n = 2^k, a(n) = a(n-1).
%C A263673 If n = p^k where p is an odd prime and k >= 1, 2*n*a(n) = p*(n+1)*a(n-1).
%C A263673 If n is even and not a prime power, 2*a(n) = a(n-1).
%C A263673 If n is odd and not a prime power, 2*n*a(n) = (n+1)*a(n-1). (End)
%H A263673 G. C. Greubel, <a href="/A263673/b263673.txt">Table of n, a(n) for n = 0..1000</a>
%F A263673 a(n) = A003418(n) / A001405(n).
%F A263673 a(n) = A048619(n-1) * A110654(n).
%F A263673 a(2*n) = A068550(n) = A099996(n) / A000984(n).
%F A263673 a(n) = A180000(n)*A152271(n). - _Peter Luschny_, Oct 23 2015
%F A263673 a(n) = (e/2)^(n + o(1)). - _Charles R Greathouse IV_, Oct 23 2015
%p A263673 a := n -> lcm(seq(k,k=1..n))/binomial(n,iquo(n,2)):
%p A263673 seq(a(n), n=0..49); # _Peter Luschny_, Oct 23 2015
%t A263673 Join[{1}, Table[LCM @@ Range[n]/Binomial[n, Floor[n/2]], {n, 1, 50}]] (* or *) Table[Product[Cyclotomic[k, 1], {k, 2, n}]/Binomial[n, Floor[n/2]], {n, 0, 50}] (* _G. C. Greubel_, Apr 17 2017 *)
%o A263673 (PARI) A263673(n) = lcm(vector(n,i,i)) / binomial(n,n\2);
%Y A263673 Cf. A068550, A180000.
%K A263673 nonn,easy
%O A263673 0,4
%A A263673 _Max Alekseyev_, Oct 23 2015