A203152 (n-1)-st elementary symmetric function of {1, 2, 2, 3, 3, 4, 4, 5, 5, ..., floor(1+n/2)}.

1, 3, 8, 28, 96, 420, 1824, 9696, 51360, 322560, 2021760, 14670720, 106323840, 875992320, 7211151360, 66526064640, 613365903360, 6265340928000, 63970228224000, 716840699904000, 8030097782784000, 97954524315648000

Offset: 1

Author

Clark Kimberling, Dec 29 2011

Keywords

• nonn

Examples

			Let esf abbreviate "elementary symmetric function". Then
0th esf of {1}:  1;
1st esf of {1,2}:  1+2 = 3;
2nd esf of {1,2,2} is 1*2 + 1*2 + 2*2 = 8.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A203153.

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:
A203152 := proc(n)
    local k ;
    L := [seq(floor(1+k/2),k=1..n)] ;
    SymmPolyn(L,n-1) ;
end proc: # R. J. Mathar, Sep 23 2016

Mathematica

f[k_] := Floor[(k + 2)/2]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}] (* A203152 *)