cp's OEIS Frontend

A024202 a(n) = [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 odd positive integers}.

%I A024202 #14 Dec 31 2016 01:02:35
%S A024202 1,11,38,96,205,385,662,1068,1635,2401,3410,4706,6339,8365,10840,
%T A024202 13826,17391,21603,26536,32270,38885,46467,55108,64900,75941,88335,
%U A024202 102186,117604,134705,153605,174426,197296,222343,249701,279510,311910,347047,385073
%N A024202 a(n) = [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 odd positive integers}.
%H A024202 Robert Israel, <a href="/A024202/b024202.txt">Table of n, a(n) for n = 1..10000</a>
%F A024202 Empirical g.f.: x*(x^4-5*x^3-7*x-1) / ((x-1)^5*(x^2+x+1)). - _Colin Barker_, Aug 15 2014
%F A024202 From _Robert Israel_, Dec 30 2016: (Start)
%F A024202 a(n) = floor(A024197(n)/(n+2)^2) = floor(n*(n+1)*(n^2+3*n+1)/6).
%F A024202 a(n) = (n^4+4*n^3+4*n^2+n-4)/6 if n == 1 (mod 3).
%F A024202 Otherwise a(n) = n*(n+1)*(n^2+3*n+1)/6.
%F A024202 The empirical g.f. can be obtained from this. (End)
%p A024202 f:= proc(n)
%p A024202   if n mod 3 = 1 then (n^4+4*n^3+4*n^2+n-4)/6
%p A024202   else n*(n+1)*(n^2+3*n+1)/6
%p A024202   fi
%p A024202 end proc:
%p A024202 map(f, [$1..100]); # _Robert Israel_, Dec 30 2016
%t A024202 Table[Floor[n*(n + 1)*(n^2 + 3*n + 1)/6], {n, 1, 50}] (* _G. C. Greubel_, Dec 30 2016 *)
%o A024202 (PARI) for(n=1,25, print1(floor(n*(n+1)*(n^2+3*n+1)/6), ", ")) \\ _G. C. Greubel_, Dec 30 2016
%Y A024202 Cf. A024197.
%K A024202 nonn
%O A024202 1,2
%A A024202 _Clark Kimberling_