with(combstruct);

#plane trees
Tspec := {T = Prod(Z,Sequence(T))};
gfseries(Tspec, unlabelled, x);

Order := 30;
Tser := gfseries(Tspec, unlabelled, x)[T(x)];
coeff(Tser, x, 24);
count([T, Tspec, unlabelled], size=24);


#partitions
Pspec := {P = Set(Sequence(Z,1 <= card))};
gfseries(Pspec, unlabelled, x); 


#words
Bspec := {B = Sequence(Union(Z1, Z2)), Z1=Atom, Z2=Atom};
gfseries(Bspec, unlabelled, x);
gfsolve(Bspec, unlabelled, x);


#can it solve the others?
gfsolve(Tspec, unlabelled, x);
gfsolve(Pspec, unlabelled, x);

#it can also generate all elements
allstructs([T, Tspec, unlabelled], size=3);
allstructs([T, Tspec, unlabelled], size=4);
allstructs([B, Bspec, unlabelled], size=3);

#or a random element
draw([T, Tspec, unlabelled], size=4);