Barbero G., J. FernandoSalas Martínez, JesúsSánchez Villaseñor, Eduardo Jesús2017-05-222017-05-222014-07Journal of Combinatorial Theory, Series A, 2014, 125, pp. 146-165.0097-3165https://hdl.handle.net/10016/24596We consider Problem 6.94 posed in the book Concrete Mathematics by Graham, Knuth, and Patashnik, and solve it by using bivariate exponential generating functions. The family of recurrence relations considered in the problem contains many cases of combinatorial interest for particular choices of the six parameters that define it. We give a complete classification of the partial differential equations satisfied by the exponential generating functions, and solve them in all cases. We also show that the recurrence relations defining the combinatorial numbers appearing in this problem display an interesting degeneracy that we study in detail. Finally, we obtain for all cases the corresponding univariate row generating polynomials.20application/pdfeng© 2014 ElsevierAtribución-NoComercial-SinDerivadas 3.0 EspañaRecurrence equationsExponential generating functionsRow generating polynomialsresearch articleMatemáticashttps://dx.doi.org/10.1016/j.jcta.2014.02.007open access146165Journal of Combinatorial Theory. Series A125AR/0000015196