A024179 Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(2+3+...+n+4)).

8, 52, 189, 526, 1242, 2609, 5024, 9043, 15411, 25108, 39392, 59842, 88414, 127496, 179963, 249241, 339377, 455103, 601915, 786146, 1015050, 1296888, 1641014, 2057967, 2559573, 3159036, 3871051, 4711904, 5699589, 6853918, 8196644, 9751581

Offset

1,1

Comments

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

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

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

Maple

SymmPolyn := proc(L::list, n::integer)
        local c, a, sel;
        a :=0 ;
        sel := combinat[choose](nops(L), n) ;
        for c in sel do
                a := a+mul(L[e], e=c) ;
        end do:
        a;
end proc:
A024179 := proc(n)
        [seq(k, k=2..n+4)] ;
        2*SymmPolyn(%, 4)/(n+6)/(n+3) ;
        floor(%) ;
end proc: # R. J. Mathar, Sep 23 2016

Mathematica

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 *)

Prog

(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

Crossrefs

Sequence in context: A302318 A035288 A303012 * A302816 A026963 A026973

Adjacent sequences: A024176 A024177 A024178 * A024180 A024181 A024182

Keyword

nonn

Author

Clark Kimberling

Status

approved