In:
from sage.combinat.q_analogues import q_int
from sage.combinat.q_analogues import q_factorial
from sage.combinat.q_analogues import q_binomial
from sage.combinat.q_analogues import q_catalan_number
print q_int(5).parent()
print q_factorial(5).parent()
print q_binomial(3,2).parent()
print q_catalan_number(5).parent()
Out:
Univariate Polynomial Ring in q over Integer Ring
Univariate Polynomial Ring in q over Integer Ring
Univariate Polynomial Ring in q over Integer Ring
Fraction Field of Univariate Polynomial Ring in q over Integer Ring
What is the reason that the q_catalan_numbers have a different type than, say, the q_factorials?