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

1, 1, 1, 2, 2, 6, 3, 12, 12, 20, 10, 60, 30, 210, 105, 56, 56, 504, 252, 2520, 1260, 660, 330, 3960, 1980, 5148, 2574, 4004, 2002, 30030, 15015, 240240, 240240, 123760, 61880, 31824, 15912, 302328, 151164, 77520, 38760, 813960, 406980, 8953560, 4476780, 2288132, 1144066, 27457584, 13728792, 49031400

Offset: 0

Author

Max Alekseyev, Oct 23 2015

Keywords

• nonn
• easy

Comments

From Robert Israel, Oct 23 2015: (Start)

If n = 2^k, a(n) = a(n-1).

If n = p^k where p is an odd prime and k >= 1, 2*n*a(n) = p*(n+1)*a(n-1).

If n is even and not a prime power, 2*a(n) = a(n-1).

If n is odd and not a prime power, 2*n*a(n) = (n+1)*a(n-1). (End)

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A068550, A180000.

Programs

Maple

a := n -> lcm(seq(k,k=1..n))/binomial(n,iquo(n,2)):
seq(a(n), n=0..49); # Peter Luschny, Oct 23 2015

Mathematica

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 *)

PARI

A263673(n) = lcm(vector(n,i,i)) / binomial(n,n\2);

Formula

a(n) = A003418(n) / A001405(n).

a(n) = A048619(n-1) * A110654(n).

a(2*n) = A068550(n) = A099996(n) / A000984(n).

a(n) = A180000(n)*A152271(n). - Peter Luschny, Oct 23 2015

a(n) = (e/2)^(n + o(1)). - Charles R Greathouse IV, Oct 23 2015