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A203154 (n-1)-st elementary symmetric function of {2, 3, 3, 4, 4, 5, 5,...,Floor[(n+4)/2]}. 3
1, 5, 21, 102, 480, 2688, 14880, 96480, 622080, 4613760, 34110720, 285586560, 2386298880, 22289541120, 207921530880, 2145056256000, 22108972032000, 249782787072000, 2820035699712000, 34637103857664000, 425205351825408000 (list; graph; refs; listen; history; text; internal format)
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: A204061 A046633 A280623 * A097175 A100284 A337168

Adjacent sequences:  A203151 A203152 A203153 * A203155 A203156 A203157

KEYWORD

nonn

AUTHOR

Clark Kimberling, Dec 29 2011

STATUS

approved

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Last modified November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)