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Integer part of (3rd elementary symmetric function of S(n))/(2nd elementary symmetric of S(n)), where S(n) = {3,4, ..., n+4}.
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%I #17 May 17 2018 17:28:34

%S 1,2,4,7,9,12,15,19,23,27,32,36,42,47,53,59,66,73,80,88,95,104,112,

%T 121,130,140,150,160,171,182,193,204,216,228,241,254,267,281,295,309,

%U 323,338,353

%N Integer part of (3rd elementary symmetric function of S(n))/(2nd elementary symmetric of S(n)), where S(n) = {3,4, ..., n+4}.

%H Ivan Neretin, <a href="/A024193/b024193.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(A024184(n)/A024183(n+1)). - _R. J. Mathar_, Sep 23 2016

%F a(n) = floor(1/2 n (7 + n) (46 + 13 n + n^2)/(144 + 41 n + 3 n^2)). - _Ivan Neretin_, May 17 2018

%e For n=2, the 3rd elementary symmetric function of (3,4,5,6) is 3*4*5 + 3*4*6 + 3*5*6 + 4*5*6 = 342, and the 2nd elementary symmetric function of (3,4,5,6) is 3*4 + 3*5 + 3*6 + 4*5 + 4*6 + 5*6 = 119. So 342/119 = 2.8739..., and a(2) = 2. - _Michael B. Porter_, May 05 2018

%t Table[Floor[1/2 x (7 + x) (46 + 13 x + x^2)/(144 + 41 x + 3 x^2)], {x, 43}] (* _Ivan Neretin_, May 02 2018 *)

%Y Cf. A024184, A024183.

%K nonn

%O 1,2

%A _Clark Kimberling_