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

%I A319382 #14 Apr 27 2019 05:22:18
%S A319382 6,10,15,20,21,28,35,36,45,55,56,66,70,78,84,91,105,120,120,126,136,
%T A319382 153,165,171,190,210,210,220,231,252,253,276,286,300,325,330,351,364,
%U A319382 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 A319382 Binomial coefficients binomial(m,k) for 2 <= k <= m/2 in sorted order.
%C A319382 In contrast to A006987, here the duplicates are not removed.  Thus 120 = binomial(10,3) = binomial(16,2) appears twice.
%H A319382 Robert Israel, <a href="/A319382/b319382.txt">Table of n, a(n) for n = 1..10000</a>
%F A319382 a(n) = binomial(A022911(n),A022912(n)).
%e A319382 The first three terms are binomial(4,2) = 6, binomial(5,2) = 10, binomial(6,2) = 15.
%p A319382 N:= 10^3: # to get terms <= N
%p A319382 Res:= NULL:
%p A319382 for n from 2 while n*(n-1)/2 <= N do
%p A319382   for k from 2 to n/2 do
%p A319382     v:= binomial(n,k);
%p A319382     if v > N then break fi;
%p A319382     Res:= Res,v
%p A319382 od od:
%p A319382 sort([Res]);
%t A319382 M = 10^3;
%t A319382 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 A319382 Cf. A003015, A006987, A022911 (values of m), A022912 (values of k).
%K A319382 nonn
%O A319382 1,1
%A A319382 _Robert Israel_, Sep 18 2018