  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
$\zeta(2n+4m+3),$ $n,m\ge 0,$ convergent at the geometric rate with ratio
$2^{-10}.$
