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A203152
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(n-1)-st elementary symmetric function of {1, 2, 2, 3, 3, 4, 4, 5, 5, ..., floor(1+n/2)}.
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5
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1, 3, 8, 28, 96, 420, 1824, 9696, 51360, 322560, 2021760, 14670720, 106323840, 875992320, 7211151360, 66526064640, 613365903360, 6265340928000, 63970228224000, 716840699904000, 8030097782784000, 97954524315648000
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
local k ;
L := [seq(floor(1+k/2), k=1..n)] ;
SymmPolyn(L, n-1) ;
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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