>
> I don't know what OmegaPolynomial is. However, if you replace it by 
> cyclotomic_polynomial, 
> it seems to work as expected, doesn't it?
>

No, it does not. You missed the question.
 

>
> sage: *def* *ib*(m, n): *return* sum(binomial(m*n-*1*, 
> m*k)*cyclotomic_polynomial(m*(k+*1*)) *for* k in (*0.*.n-*1*))
>
> sage: ib(*2*,*2*)
>
> 3*x^2 + x + 4
>
> sage: type(ib(*2*,*2*))
>
> <type 
> 'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>
>
> sage: ib(*2*,*2*).list()
> [4, 1, 3]
>

Execute 
    for n in (0..6): print(ib(2, n).list()
as indicated.
  

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