On extending "holonomicity"

Differential polynomials of degree at most 1 annihilates univariate holonomic functions. In this talk, I will consider functions annihilated by differential polynomials of degree at most 2. It turns out that we can describe them with a finite amount of data. Therefore they provide a computational framework for a particular class of non-holonomic functions, including the generating functions of several sequences like the Bernoulli numbers, the Euler numbers, the numbers of alternating permutations of n letters, the evaluations of the zeta function at even integers, and many more.