René Thom's 1954 paper Quelques propriétés globales des variétés differentiables calculated the unoriented cobordism ring as a free polynomial algebra over 𝔽2 with a single generator in each degree k such that k + 1 is not a power of 2. Hence the size of the cobordism group in dimension n is a modified partition function. This calculator computes this function given n.
Answer: dim𝔽2 Ωn = _.
Under cobordism, closed, unoriented manifolds with a principal ℤ/2-bundle form a ring. Thom's work identifies this group with π*(MO ∧ Bℤ/2+), which can be computed in a similar manner as above.
Answer: dim𝔽2 πn(MO ∧ Bℤ/2+) = _.
Novikov's 1960 paper Some problems in the topology of manifolds connected with the theory of Thom spaces uses Thom's construction to calculate that the cobordism ring of stably almost complex manifolds is a free polynomial algebra over ℤ. Again, the size of the cobordism group in dimension n is a modified partition function, computed in a similar way.
Answer: dimℤ πn(MU) = _.