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A203153 (n-1)-st elementary symmetric function of {2, 2, 3, 3, 4, 4, 5, 5, ..., floor((n+3)/2)}.

%I A203153 #18 Nov 28 2017 03:27:21
%S A203153 1,4,16,60,276,1248,6816,36960,236160,1503360,11041920,80922240,
%T A203153 672779520,5585448960,51894743040,481684008960,4948521984000,
%U A203153 50802038784000,571990616064000,6436746860544000,78834313248768000,965131970052096000
%N A203153 (n-1)-st elementary symmetric function of {2, 2, 3, 3, 4, 4, 5, 5, ..., floor((n+3)/2)}.
%H A203153 Clark Kimberling, <a href="/A203153/b203153.txt">Table of n, a(n) for n = 1..999</a>
%e A203153 Let esf abbreviate "elementary symmetric function". Then
%e A203153 0th esf of {2}:  1;
%e A203153 1st esf of {2,2}:  2+2 = 4;
%e A203153 2nd esf of {2,2,3} is 2*2 + 2*3 + 2*3 = 16.
%p A203153 SymmPolyn := proc(L::list,n::integer)
%p A203153     local c,a,sel;
%p A203153     a :=0 ;
%p A203153     sel := combinat[choose](nops(L),n) ;
%p A203153     for c in sel do
%p A203153         a := a+mul(L[e],e=c) ;
%p A203153     end do:
%p A203153     a;
%p A203153 end proc:
%p A203153 A203153 := proc(n)
%p A203153     [seq(floor((k+3)/2),k=1..n)] ;
%p A203153     SymmPolyn(%,n-1) ;
%p A203153 end proc: # _R. J. Mathar_, Sep 23 2016
%t A203153 f[k_] := Floor[(k + 3)/2]; t[n_] := Table[f[k], {k, 1, n}]
%t A203153 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203153 Table[a[n], {n, 1, 22}] (* A203153 *)
%Y A203153 Cf. A203152, A203154.
%K A203153 nonn
%O A203153 1,2
%A A203153 _Clark Kimberling_, Dec 29 2011