Istituto di Matematica "Guido Castelnuovo", Universita degli Studi
di Roma "La Sapienza", 00185 Roma, Italia
Abstract. Computation of generating functions for renewal sequences is performed by means of the multivariate Lagrange expansion formulae dus to Good (1960), which yields the multifold analogue of Carlitz mixed generating function. As applications, the natural transition is demonstrated from Euler's binomial theorem and the classical Vandermonde convolution formula to Abel identities and Hagen-Rothe formulas, as well as their multifold analogues due to Mohanty & Handa (1969) and Carlitz (1977), respectively.
1991 Mathematics Subject Classification. 05A14, 05A19.
Key words and phrases. Binomial coefficients, multinomial coefficients, Vandermonde convolutions, generating functions, Lagrange inversion formulae.