%I
%S 2,3,5,9,15,21,45,57,117,243,395,465,879,1053,2039,5949,10325,11739,
%T 21345,22005,64917,132167,187681,252531,775059,1215147,2126091,
%U 3883077,6003423,8207583,19058065,21162879,46406677,70113033,100115753,280588533,699418771,838568259
%N Number of distinct values of Sum_{i=0..n} x(i)*binomial(n,i), where the x(i) is a vector of length n+1 that runs through all combinations of {0, 1}.
%t a[n_] := Length @ Union[Total /@ Subsets[Table[Binomial[n, k], {k, 0, n}]]]; Array[a, 10, 0] (* _Amiram Eldar_, Jan 11 2019 *)
%o (PARI) padbin(k, n) = my(p = Pol(binary(k))); vector(n, k, polcoeff(p, k1));
%o thebins(n) = vector(2^n, k, padbin(k1, n));
%o a(n) = my(vv = thebins(n+1)); #Set(vector(#vv, k, sum(i=0, n, vv[k][i+1]*binomial(n, i)))); \\ _Michel Marcus_, Jan 11 2019
%Y Cf. A007318, A205537, A205538, A205539, A205540, A205541.
%Y Column 1 of A205542.
%K nonn
%O 0,1
%A _R. H. Hardin_, Jan 28 2012
%E Value range in title corrected and a(29)a(31) added by _Aaron Meyerowitz_, Jun 13 2014
%E a(32)a(37) from _Bert Dobbelaere_, Sep 15 2019
