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%I #17 Sep 08 2022 08:44:48
%S 1,3,5,9,13,18,24,30,37,45,54,64,74,85,97,109,122,136,151,167,183,200,
%T 218,236,255,275,296,318,340,363,387,411,436,462,489,517,545,574,604,
%U 634,665,697,730,764,798,833,869,905,942,980,1019,1059,1099,1140,1182,1224
%N [ (4th elementary symmetric function of S(n))/(3rd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 2 mod 3}.
%H Vincenzo Librandi, <a href="/A024403/b024403.txt">Table of n, a(n) for n = 1..5000</a>
%F Empirical g.f.: x*(x^2-x+1)*(x^8-x^7-x^5+x^4-x^3-x-1) / ((x-1)^3*(x^2+1)*(x^4+1)). - _Colin Barker_, Aug 16 2014
%F a(n) = floor(A024393(n) / A024392(n + 1)). - _Sean A. Irvine_, Jul 07 2019
%t Table[Floor[(n (405 n^4 + 4590 n^3 + 18495 n^2 + 30534 n + 16376)) / (40 (3 n + 10) (9 (n+1)^2 + 33 n + 55))], {n, 1, 100}] (* _Vincenzo Librandi_, Jul 07 2019 *)
%o (Magma) [(n*(405*n^4+4590*n^3+18495*n^2+30534*n+16376)) div (40*(3*n+10)*(9*(n+1)^2+33*n+55)): n in [1..60]]; // _Vincenzo Librandi_, Jul 07 2019
%Y Cf. A024392, A024393.
%K nonn
%O 1,2
%A _Clark Kimberling_
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