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A319382
Binomial coefficients binomial(m,k) for 2 <= k <= m/2 in sorted order.
3
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
1,1
COMMENTS
In contrast to A006987, here the duplicates are not removed. Thus 120 = binomial(10,3) = binomial(16,2) appears twice.
LINKS
FORMULA
a(n) = binomial(A022911(n),A022912(n)).
EXAMPLE
The first three terms are binomial(4,2) = 6, binomial(5,2) = 10, binomial(6,2) = 15.
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 *)
CROSSREFS
Cf. A003015, A006987, A022911 (values of m), A022912 (values of k).
Sequence in context: A145286 A315248 A315249 * A006987 A182237 A337612
KEYWORD
nonn
AUTHOR
Robert Israel, Sep 18 2018
STATUS
approved