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

1, 4, 31, 486, 15381, 978768, 124918731, 31932406170, 16337382642945, 16723323142761060, 34243057328337866295, 140246638967945496322350, 1148847521944847479468879725, 18822284044001939139425413111800, 616761496621711735518439444437389475

Offset: 1

Author

Clark Kimberling, Dec 29 2011

Keywords

• nonn

Links

• Clark Kimberling, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A122743.

Programs

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:
A203011 := proc(n)
    local L,k ;
    L := [seq(2^k-1,k=1..n)] ;
    SymmPolyn(L,n-1) ;
end proc: # R. J. Mathar, Sep 23 2016

Mathematica

f[k_] := -1 + 2^k; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 16}] (* 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 *)

Formula

a(n) = c * 2^(n*(n+1)/2), where c = A048651 * A065442 = 0.4639944324508904477884... . - Vaclav Kotesovec, Oct 10 2016