\\Computes a(n) and if you uncomment the printstatements, prints the products for which the result
\\occurs just once. Works for n < 9 for me due to memory restrictions. 
a(n) = {my(r=vector(binomial(2*n-1,n-1)),p,t,q);
forvec(v=vector(n,i,[1,n]),
	q++;p=prod(i=1,#v,v[i]);
	r[q]=[p,v]
,
1
);r=vecsort(r);

\\If you want to see the vector resulting in this unique product, uncomment the following statement:
\\print(r[1]);

\\If you want to see the vector resulting in this unique product, 
\\and the frequency of each factor, uncomment the following statement:
\\print(r[1]" "freq(r[1][2]));

for(i=2,#r-1,
	if(r[i-1][1]!=r[i][1]&&r[i][1]!=r[i+1][1],
		t++;
\\If you want to see the vector resulting in this unique product, uncomment the following statement:
		\\print(r[i]);
\\If you want to see the vector resulting in this unique product, 
\\and the frequency of each factor, uncomment the following statement:
		\\print(r[i]" "freq(r[i][2]));
	)	
);
if(n>1,
\\If you want to see the vector resulting in this unique product, uncomment the following statement:
	\\print(r[#r]);
\\If you want to see the vector resulting in this unique product, 
\\and the frequency of each factor, uncomment the following statement:
	print(r[#r]" "freq(r[#r][2]));
	t+2
	,
	t+1
)
} 

\\ function returns a vector r that tells how often an element i occurs in a vector v, 1 <= i <= #r. 
freq(v) = {my(r = vector(#v));
	for(i=1,#v,r[v[i]]++);r
}