A203153 (n-1)-st elementary symmetric function of {2, 2, 3, 3, 4, 4, 5, 5, ..., floor((n+3)/2)}.

1, 4, 16, 60, 276, 1248, 6816, 36960, 236160, 1503360, 11041920, 80922240, 672779520, 5585448960, 51894743040, 481684008960, 4948521984000, 50802038784000, 571990616064000, 6436746860544000, 78834313248768000, 965131970052096000

Offset: 1

Author

Clark Kimberling, Dec 29 2011

Keywords

• nonn

Examples

			Let esf abbreviate "elementary symmetric function". Then
0th esf of {2}:  1;
1st esf of {2,2}:  2+2 = 4;
2nd esf of {2,2,3} is 2*2 + 2*3 + 2*3 = 16.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..999

Crossrefs

Cf. A203152, A203154.

Programs

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:
A203153 := proc(n)
    [seq(floor((k+3)/2),k=1..n)] ;
    SymmPolyn(%,n-1) ;
end proc: # R. J. Mathar, Sep 23 2016

Mathematica

f[k_] := Floor[(k + 3)/2]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}] (* A203153 *)