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A203011 (n-1)-st elementary symmetric function of {1,3,7,15,31,63,...-1+2^n}.

%I A203011 #20 Feb 23 2018 10:48:17
%S A203011 1,4,31,486,15381,978768,124918731,31932406170,16337382642945,
%T A203011 16723323142761060,34243057328337866295,140246638967945496322350,
%U A203011 1148847521944847479468879725,18822284044001939139425413111800,616761496621711735518439444437389475
%N A203011 (n-1)-st elementary symmetric function of {1,3,7,15,31,63,...-1+2^n}.
%H A203011 Clark Kimberling, <a href="/A203011/b203011.txt">Table of n, a(n) for n = 1..50</a>
%F A203011 a(n) = c * 2^(n*(n+1)/2), where c = A048651 * A065442 = 0.4639944324508904477884... . - _Vaclav Kotesovec_, Oct 10 2016
%p A203011 SymmPolyn := proc(L::list,n::integer)
%p A203011     local c,a,sel;
%p A203011     a :=0 ;
%p A203011     sel := combinat[choose](nops(L),n) ;
%p A203011     for c in sel do
%p A203011         a := a+mul(L[e],e=c) ;
%p A203011     end do:
%p A203011     a;
%p A203011 end proc:
%p A203011 A203011 := proc(n)
%p A203011     local L,k ;
%p A203011     L := [seq(2^k-1,k=1..n)] ;
%p A203011     SymmPolyn(L,n-1) ;
%p A203011 end proc: # _R. J. Mathar_, Sep 23 2016
%t A203011 f[k_] := -1 + 2^k; t[n_] := Table[f[k], {k, 1, n}]
%t A203011 a[n_] := SymmetricPolynomial[n - 1, t[n]]
%t A203011 Table[a[n], {n, 1, 16}] (* A203011 *)
%t A203011 Table[Product[2^k-1,{k,1,n}] * Sum[1/(2^k-1),{k,1,n}],{n,1,16}] (* _Vaclav Kotesovec_, Sep 06 2014 *)
%Y A203011 Cf. A122743.
%K A203011 nonn
%O A203011 1,2
%A A203011 _Clark Kimberling_, Dec 29 2011