login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048619 a(n) = LCM(binomial(n,0), ..., binomial(n,n)) / binomial(n,floor(n/2)). 4

%I

%S 1,1,1,1,2,1,3,3,4,2,10,5,30,15,7,7,56,28,252,126,60,30,330,165,396,

%T 198,286,143,2002,1001,15015,15015,7280,3640,1768,884,15912,7956,3876,

%U 1938,38760,19380,406980,203490,99484,49742,1144066,572033,1961256,980628

%N a(n) = LCM(binomial(n,0), ..., binomial(n,n)) / binomial(n,floor(n/2)).

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

%F a(n) = A002944(n)/A001405(n).

%F a(n) = lcm(1..n+1)/(floor((n+3)/2)*binomial(n+1,floor((n+3)/2)). - _Paul Barry_, Jul 03 2006

%F a(n) = lcm(1,2,...,n+1) / (ceiling((n+1)/2)*binomial(n+1,floor((n+1)/2))) = A003418(n+1) / A100071(n+1). - _Max Alekseyev_, Oct 23 2015

%F a(n) = A263673(n+1) / A110654(n+1) = A180000(n+1) / A152271(n). - _Max Alekseyev_, Oct 23 2015

%F a(2*n-1) = A068553(n) = A068550(n)/n.

%e If n=10 then A002944(10)=2520, A001405(10)=252, the quotient a(10)=10.

%t Table[Apply[LCM, Binomial[n, Range[0, n]]]/Binomial[n, Floor[n/2]], {n, 0, 48}] (* _Michael De Vlieger_, Jun 29 2017 *)

%o (PARI) {A048619(n) = lcm(vector(n+1, i, i)) / binomial(n+1, (n+1)\2) / ((n+2)\2);}

%o (MAGMA) [Lcm([1..n+1]) div (Floor((n+3)/2)*Binomial(n+1,Floor((n+3)/2))): n in [0..50]]; // _Vincenzo Librandi_, Jul 10 2019

%Y Cf. A001405, A002944.

%K nonn,easy

%O 0,5

%A _Labos Elemer_

%E Definition corrected and a(0)=1 prepended by _Max Alekseyev_, Oct 23 2015

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)