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.
%I A048618 #21 Jan 23 2025 15:49:03 %S A048618 2,4,12,30,40,56,84,90,132,154,176,182,208,220,252,280,306,312,340, %T A048618 374,380,408,418,420,440,456,462,476,480,532,552,598,616,624,630,644, %U A048618 650,660,690,736,756,828,840,858,870,880,884,900,918,920,928,936,952,966 %N A048618 Even numbers n such that binomial(n,n/2) is divisible by n/2. %H A048618 Rémy Sigrist, <a href="/A048618/b048618.txt">Table of n, a(n) for n = 1..10000</a> %H A048618 M. Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP Scripts for Miscellaneous Math Problems</a>, sect. III: Binomial coefficients modulo integers, binomod.gp (V. 1.4, 11/2015). %F A048618 a(n) = 2 * A014847(n). - _Rémy Sigrist_, Aug 27 2017 %e A048618 For n=30, binomial(30,15) = 155117520 = 15^10341168, so 30 is a term. %p A048618 a:=[]; %p A048618 for n from 1 to 1000 do if ( binomial(2*n,n) mod n ) = 0 then a:=[op(a),2*n]; fi; od; %p A048618 a; # _N. J. A. Sloane_, Aug 03 2017 %t A048618 Select[Range[2,1000,2],Mod[Binomial[#,#/2],#/2]==0&] (* _Harvey P. Dale_, Jan 23 2025 *) %Y A048618 Cf. A001405, A020475, A014847, A067348 (binomial(2*n,n) is divisible by 2*n). %K A048618 nonn %O A048618 1,1 %A A048618 _Labos Elemer_ %E A048618 Definition corrected by _N. J. A. Sloane_, Aug 03 2017