{o=_
for(n=NF;i=N=n--;o=k?o(o?k<0?FS:" +":_)k(n?"x^"n:_):o){a=$0
for(f=1;--i;f*=i)for(m=N;1<M=m--;)$M-=$m
k=$N/f
for($0=a;--N;)$N-=k*N^n}$0=o}gsub(/1?x(.1)?/,"x")
Note that non-ascii characters in the above source code will be escaped (such as \x9f).