closed forms of [q^m]U1..U4 agree with exact series for m<=80: True
negative Taylor coefficients of Omega for m,n<=80: 0
[q^5 x^0] Omega = 1/6 (>0)
n=1 closed form (m>=2): m![q^m](U2+U3) = (m+1)((m-4)2^{m-2}+2): True
n=2 bound (all m>=0): m![q^m](2U1+U2) = 2^{m-2}(m^2-m-8)+2(m+1): True
values of 2^{m-2}(m^2-m-8)+2(m+1), m=0..6: [Fraction(0, 1), Fraction(0, 1), Fraction(0, 1), Fraction(4, 1), Fraction(26, 1), Fraction(108, 1), Fraction(366, 1)]
