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

%I A203152 #19 Nov 28 2017 03:27:13
%S A203152 1,3,8,28,96,420,1824,9696,51360,322560,2021760,14670720,106323840,
%T A203152 875992320,7211151360,66526064640,613365903360,6265340928000,
%U A203152 63970228224000,716840699904000,8030097782784000,97954524315648000
%N A203152 (n-1)-st elementary symmetric function of {1, 2, 2, 3, 3, 4, 4, 5, 5, ..., floor(1+n/2)}.
%H A203152 Clark Kimberling, <a href="/A203152/b203152.txt">Table of n, a(n) for n = 1..1000</a>
%e A203152 Let esf abbreviate "elementary symmetric function". Then
%e A203152 0th esf of {1}:  1;
%e A203152 1st esf of {1,2}:  1+2 = 3;
%e A203152 2nd esf of {1,2,2} is 1*2 + 1*2 + 2*2 = 8.
%p A203152 SymmPolyn := proc(L::list,n::integer)
%p A203152     local c,a,sel;
%p A203152     a :=0 ;
%p A203152     sel := combinat[choose](nops(L),n) ;
%p A203152     for c in sel do
%p A203152         a := a+mul(L[e],e=c) ;
%p A203152     end do:
%p A203152     a;
%p A203152 end proc:
%p A203152 A203152 := proc(n)
%p A203152     local k ;
%p A203152     L := [seq(floor(1+k/2),k=1..n)] ;
%p A203152     SymmPolyn(L,n-1) ;
%p A203152 end proc: # _R. J. Mathar_, Sep 23 2016
%t A203152 f[k_] := Floor[(k + 2)/2]; t[n_] := Table[f[k], {k, 1, n}]
%t A203152 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203152 Table[a[n], {n, 1, 22}] (* A203152 *)
%Y A203152 Cf. A203153.
%K A203152 nonn
%O A203152 1,2
%A A203152 _Clark Kimberling_, Dec 29 2011