cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A068550 a(n) = lcm{1, ..., 2n} / binomial(2n, n).

This page as a plain text file.
%I A068550 #23 Mar 06 2022 08:38:16
%S A068550 1,1,2,3,12,10,30,105,56,252,1260,330,1980,2574,2002,15015,240240,
%T A068550 61880,15912,151164,38760,406980,4476780,1144066,13728792,24515700,
%U A068550 6249100,84362850,21474180,5462730,81940950,1270084725,645122400
%N A068550 a(n) = lcm{1, ..., 2n} / binomial(2n, n).
%C A068550 Known to be always an integer.
%H A068550 Hojoo Lee, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;2e3bb004.0202">Re: LCM [1,2,..,N] > 2^{N-1}</a>, NMBRTHRY Mailing List, Feb 18 2002.
%H A068550 Daniel Ropp, <a href="https://cms.math.ca/publications/crux/issue?volume=13&amp;issue=10">Solution to Problem 31</a>, Crux Mathematicorum, Vol. 13, No. 10 (1987), p. 314.
%F A068550 a(n) = A099996(n) / A000984(n) = A003418(2*n) / A001405(2*n) = A180000(2*n) = A263673(2*n).
%F A068550 a(n) = n * A068553(n) = n * A048619(2*n-1).
%t A068550 a[0] = 1; a[n_] := (LCM @@ Range[2*n])/Binomial[2*n, n]; Array[a, 33, 0] (* _Amiram Eldar_, Mar 06 2022 *)
%o A068550 (PARI) a(n) = lcm([1..2*n])/binomial(2*n, n); \\ _Michel Marcus_, Mar 06 2022
%Y A068550 Bisection of A180000 and A263673.
%K A068550 nonn,easy
%O A068550 0,3
%A A068550 _N. J. A. Sloane_, Mar 23 2002
%E A068550 a(0)=1 prepended by _Max Alekseyev_, Oct 23 2015