A319382 Binomial coefficients binomial(m,k) for 2 <= k <= m/2 in sorted order.

6, 10, 15, 20, 21, 28, 35, 36, 45, 55, 56, 66, 70, 78, 84, 91, 105, 120, 120, 126, 136, 153, 165, 171, 190, 210, 210, 220, 231, 252, 253, 276, 286, 300, 325, 330, 351, 364, 378, 406, 435, 455, 462, 465, 495, 496, 528, 560, 561, 595, 630, 666, 680, 703, 715, 741, 780, 792, 816, 820, 861, 903, 924

Offset: 1

Author

Robert Israel, Sep 18 2018

Keywords

• nonn

Comments

In contrast to A006987, here the duplicates are not removed. Thus 120 = binomial(10,3) = binomial(16,2) appears twice.

Examples

			The first three terms are binomial(4,2) = 6, binomial(5,2) = 10, binomial(6,2) = 15.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003015, A006987, A022911 (values of m), A022912 (values of k).

Programs

Maple

N:= 10^3: # to get terms <= N
Res:= NULL:
for n from 2 while n*(n-1)/2 <= N do
  for k from 2 to n/2 do
    v:= binomial(n,k);
    if v > N then break fi;
    Res:= Res,v
od od:
sort([Res]);

Mathematica

M = 10^3;
Reap[For[n = 2, n(n-1)/2 <= M, n++, For[k = 2, k <= n/2, k++, v = Binomial[n, k]; If[v > N, Break[]]; Sow[v]]]][[2, 1]] // Sort (* Jean-François Alcover, Apr 27 2019, from Maple *)

Formula

a(n) = binomial(A022911(n),A022912(n)).