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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..502
Programs
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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 *)