A024179 - OEIS

%I #16 May 21 2018 08:47:37

%S 8,52,189,526,1242,2609,5024,9043,15411,25108,39392,59842,88414,

%T 127496,179963,249241,339377,455103,601915,786146,1015050,1296888,

%U 1641014,2057967,2559573,3159036,3871051,4711904,5699589,6853918,8196644,9751581

%N Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(2+3+...+n+4)).

%C The 4th elementary symmetric function of 2,3,..n+4 is the polynomial n*(n+1)*(n+2)*(n+3)*(15*n^4+330*n^3+2765*n^2+10482*n+15208)/5760. The denominator is (n+3)*(n+6)/2. The sequence is the rounded down ratio of both. - _R. J. Mathar_, Oct 01 2016

%H Ivan Neretin, <a href="/A024179/b024179.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(1/2880 n (n+1) (n+2) (15 n^4 + 330 n^3 + 2765 n^2 + 10482 n + 15208)/(n + 6)). - _Muniru A Asiru_, May 20 2018

%p SymmPolyn := proc(L::list,n::integer)

%p         local c,a,sel;

%p         a :=0 ;

%p         sel := combinat[choose](nops(L),n) ;

%p         for c in sel do

%p                 a := a+mul(L[e],e=c) ;

%p         end do:

%p         a;

%p end proc:

%p A024179 := proc(n)

%p         [seq(k,k=2..n+4)] ;

%p         2*SymmPolyn(%,4)/(n+6)/(n+3) ;

%p         floor(%) ;

%p end proc: # _R. J. Mathar_, Sep 23 2016

%t Table[Floor[1/2880 n (n + 1) (n + 2) (15 n^4 + 330 n^3 + 2765 n^2 + 10482 n + 15208)/(n + 6)], {n, 32}] (* _Ivan Neretin_, May 20 2018 *)

%o (GAP) List([1..40],n->Int((1/2880)*n*(n+1)*(n+2)*(15*n^4+330*n^3+2765*n^2+10482*n+15208)/(n+6))); # _Muniru A Asiru_, May 20 2018

%K nonn

%O 1,1

%A _Clark Kimberling_