We prove generating function identities producing fast convergent series for the sequences β(2n+1), β(2n+2) and β(2n+3), where β is Dirichlet's beta function. In particular, we obtain a new accelerated series for Catalan's constant convergent at a geometric rate with ratio 2^-10, which can be considered as an analog of Amdeberhan-Zeilberger's series for ζ(3).