with(GraphTheory):
with(combinat):

OCP_STAR :=
proc(part)
option remember;
local mset;

    mset := convert(part, `multiset`);

    expand('k'*mul(binomial(('k'-1)^item[1]+item[2]-1,
                            item[2]),
                   item in mset));
end;

Y := (part, kval) -> subs('k'=kval, OCP_STAR(part));

YSEQ :=
proc(mx, k)
    local n, part, res;

    res := [];

    for n from 0 to mx do
        part := firstpart(n);

        while type(part, `list`) do
            res :=
            [op(res), Y(part, k)];

            part := nextpart(part);
        od;
    od;

    res;
end;