A048618 Even numbers n such that binomial(n,n/2) is divisible by n/2.

2, 4, 12, 30, 40, 56, 84, 90, 132, 154, 176, 182, 208, 220, 252, 280, 306, 312, 340, 374, 380, 408, 418, 420, 440, 456, 462, 476, 480, 532, 552, 598, 616, 624, 630, 644, 650, 660, 690, 736, 756, 828, 840, 858, 870, 880, 884, 900, 918, 920, 928, 936, 952, 966

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			For n=30, binomial(30,15) = 155117520 = 15^10341168, so 30 is a term.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• M. Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems, sect. III: Binomial coefficients modulo integers, binomod.gp (V. 1.4, 11/2015).

Crossrefs

Cf. A001405, A020475, A014847, A067348 (binomial(2*n,n) is divisible by 2*n).

Programs

Maple

a:=[];
for n from 1 to 1000 do if ( binomial(2*n,n) mod n ) = 0 then a:=[op(a),2*n]; fi; od;
a;   # N. J. A. Sloane, Aug 03 2017

Mathematica

Select[Range[2,1000,2],Mod[Binomial[#,#/2],#/2]==0&] (* Harvey P. Dale, Jan 23 2025 *)

Formula

a(n) = 2 * A014847(n). - Rémy Sigrist, Aug 27 2017

Extensions

Definition corrected by N. J. A. Sloane, Aug 03 2017