{ g(t) = if(t<0, return(0)); if(t==0,1,2^(t-1)); }
{ f(n,m) = my(r=0); if(#m==0,return(g(n))); forvec(s=vector(#m,i,[0,(m[i]-1)2]), r += prod(i=0,#m, g(if(i<#m,s[i+1],n)-if(i>0,m[i]-s[i],0));); ,2); r; }
{ F(n) = my(r=0); for(k=0,2*n-1, forvec(m=vector(k,i,[1,2*n-1]), r+=(-1)^k*f(n,m)^2; ,2); ); r; }