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By application of the Markov-WZ method, we prove a more general form of a bivariate generating function identity containing, as particular cases, Koecher's and Almkvist-Granville's Ap'ery-like formulae for odd zeta values. As a consequence, we get a new identity producing Ap'ery-like series for all zeta(2n+4m+3),n,mge0, convergent at the geometric rate with ratio $2^{-10}.
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