A024185 Fourth elementary symmetric function of 3,4,...,n+5.

360, 2754, 12154, 40369, 111769, 271929, 600033, 1225983, 2353263, 4288713, 7480473, 12565462, 20427862, 32270182, 49698582, 74824242, 110382666, 159872916, 227718876, 319454751, 441937111, 603585895, 814656895, 1087548345, 1437144345

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Programs

GAP

List([1..30],n->n*(n+1)*(n+2)*(n+3)*(15*n^4+450*n^3+5165*n^2+26922*n+53848)/5760); # Muniru A Asiru, May 19 2018

Maple

S := proc(n,L) mul(x+i,i=L) ; expand(%) ; coeftayl(%,x=0,nops(L)-n) ; end:
A024185 := proc(n) S(4,[seq(j,j=3..n+5)]) ; end: seq(A024185(n),n=1..40) ; # R. J. Mathar, Sep 15 2009

Formula

G.f.: x*(360-486*x+328*x^2-113*x^3+16*x^4)/(1-x)^9. - R. J. Mathar, Sep 15 2009

a(n) = n*(n+1)*(n+2)*(n+3)*(15*n^4+450*n^3+5165*n^2+26922*n+53848)/5760. - R. J. Mathar, Sep 15 2009

Extensions

Variable set in definition changed by R. J. Mathar, Sep 15 2009