A203154 (n-1)-st elementary symmetric function of {2, 3, 3, 4, 4, 5, 5,...,Floor[(n+4)/2]}.

1, 5, 21, 102, 480, 2688, 14880, 96480, 622080, 4613760, 34110720, 285586560, 2386298880, 22289541120, 207921530880, 2145056256000, 22108972032000, 249782787072000, 2820035699712000, 34637103857664000, 425205351825408000

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..502

Example

Let esf abbreviate "elementary symmetric function". Then
0th esf of {2}:  1
1st esf of {2,3}:  2+3=5;
2nd esf of {2,3,3} is 2*3+2*3+3*3=21.

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:
A203154 := proc(n)
    [seq(floor((k+4)/2), k=1..n)] ;
    SymmPolyn(%, n-1);
end proc:  # R. J. Mathar, Sep 23 2016
# second Maple program:
f:=  proc(n) local L, x;
  if n::odd then L:= `*`(x+2, seq((x+i)$2, i=3..2+n/2))
  else L:= `*`(seq((x+i)*(x+i+1), i=2..1+n/2))
  fi;
  coeff(L, x, 1);
end proc:
map(f, [$1..50]); # Robert Israel, Nov 27 2017

Mathematica

f[k_] := Floor[(k + 4)/2]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}] (* A203154 *)

Crossrefs

Cf. A203152, A203153, A203155.

Sequence in context: A362556 A046633 A280623 * A097175 A100284 A337168

Adjacent sequences: A203151 A203152 A203153 * A203155 A203156 A203157

Keyword

nonn

Author

Clark Kimberling, Dec 29 2011

Status

approved