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A024179 Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(2+3+...+n+4)). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 19 00:55 EDT 2019. Contains 324217 sequences. (Running on oeis4.)