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A024174 a(n) is floor((4th elementary symmetric function of 1,2,..,n)/(3rd elementary symmetric function of 1,2,...,n)).

%I A024174 #53 Oct 28 2021 02:06:19
%S A024174 0,0,1,2,3,4,6,8,10,13,16,19,22,25,29,33,37,42,47,52,57,62,68,74,80,
%T A024174 87,94,101,108,115,123,131,139,148,157,166,175,184,194,204,214,225,
%U A024174 236,247,258,269,281,293,305,318,331,344,357,370,384,398,412,427,442
%N A024174 a(n) is floor((4th elementary symmetric function of 1,2,..,n)/(3rd elementary symmetric function of 1,2,...,n)).
%H A024174 Ivan Neretin, <a href="/A024174/b024174.txt">Table of n, a(n) for n = 3..10000</a>
%F A024174 Empirical g.f.: x^5*(x^7-2*x^6+2*x^5-2*x^4+x^3-x^2+x-1) / ((x-1)^3*(x^2+1)*(x^4+1)). - _Colin Barker_, Aug 16 2014
%F A024174 a(n) = floor( A000915(n-3)/A001303(n-2) ). - _R. J. Mathar_, Sep 23 2016
%F A024174 a(n) = floor((n - 3)*(15n^3 + 15n^2 - 10n - 8)/(120*n*(n + 1))). - _Ivan Neretin_, Nov 25 2016
%F A024174 a(n) = floor((A000217(n-2)/2 - 1)/2) = floor((n^2 - 3*n - 2)/8), n >= 4. - _Ralf Steiner_, Oct 25 2021
%e A024174 G.f. = x^5 + 2*x^6 + 3*x^7 + 4*x^8 + 6*x^9 + 8*x^10 + 10*x^11 + 13*x^12 + ...
%t A024174 Table[Floor[(n - 3) (15 n^3 + 15 n^2 - 10 n - 8)/(120 n (n + 1))], {n, 3, 45}] (* _Ivan Neretin_, Nov 25 2016 *)
%t A024174 Insert[Table[Floor[1/8 (-2 - 3 n + n^2)], {n, 4, 45}], 0, 1] (* _Ralf Steiner_, Oct 27 2021 *)
%o A024174 (PARI) {a(n) = if( n<4, 0, (n-3) * (15*n^3 + 15*n^2 - 10*n - 8) \ (120 * n * (n+1)))}; /* _Michael Somos_, Nov 25 2016 */
%Y A024174 Cf. A000915, A001303, A011848, A000217.
%K A024174 nonn
%O A024174 3,4
%A A024174 _Clark Kimberling_
%E A024174 Offset set to 3 by _R. J. Mathar_, Sep 23 2016