I figured out what was going on. It seems the sym interpreter was giving a rational approximation for pi only some of the time. Very strange. For future reference, this is how I got what is expected:
syms f0 T t0 Omegan t n
p = sym(pi); % Key step here.
simplify(subs(2*f0*p^2/(Omegan*T*(- Omegan^2*t0^2 + 4*p^2)),Omegan,2*n*p/T))
-(T^2*f0)/(4*n*pi*(- T^2 + n^2*t0^2))