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Binomial coefficients binomial(m,k) for 2 <= k <= m/2 in sorted order.
3

%I #14 Apr 27 2019 05:22:18

%S 6,10,15,20,21,28,35,36,45,55,56,66,70,78,84,91,105,120,120,126,136,

%T 153,165,171,190,210,210,220,231,252,253,276,286,300,325,330,351,364,

%U 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

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

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

%H Robert Israel, <a href="/A319382/b319382.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%p N:= 10^3: # to get terms <= N

%p Res:= NULL:

%p for n from 2 while n*(n-1)/2 <= N do

%p for k from 2 to n/2 do

%p v:= binomial(n,k);

%p if v > N then break fi;

%p Res:= Res,v

%p od od:

%p sort([Res]);

%t M = 10^3;

%t 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 *)

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

%K nonn

%O 1,1

%A _Robert Israel_, Sep 18 2018