constant MAX_N = 32,
         BRANCH = 4

sequence {rooted,unrooted} @= repeat(0,MAX_N+2)

procedure tree(integer br, n, l=n, tot=1, atom cnt=1)
atom c
    for b=br+1 to BRANCH do
        tot += n
        if tot>=MAX_N+1
        or (l*2>=tot and b>=BRANCH) then
            return
        end if
        if b==br+1 then
            c = rooted[n+1]*cnt
        else
            c *= (rooted[n+1]+(b-br-1))/(b-br)
        end if
        if l*2<tot then
            unrooted[tot+1] += c
        end if
        if b<BRANCH then
            rooted[tot+1] += c
            for m=1 to n-1 do
                tree(b,m,l,tot,c)
            end for
        end if
    end for
end procedure

procedure bicenter(integer s)
    if mod(s,2)=0 then
        atom aux = rooted[s/2+1]
        unrooted[s+1] += aux*(aux+1)/2
    end if
end procedure

rooted[1..2] = 1
unrooted[1..2] = 1
for n=1 to MAX_N do
    tree(0, n)
    bicenter(n)
    if n<10 or n=MAX_N then
        printf(1,"%d: %d\n",{n, unrooted[n+1]})
    end if
end for