@**article**{RISC419,author = {S. Gerhold},

title = {{On Some Non-Holonomic Sequences}},

language = {english},

abstract = {A sequence of complex numbers is holonomic if it satisfies a linear recurrence with
polynomial coefficients. A power series is holonomic if it satisfies
a linear differential equation with polynomial coefficients, which is
equivalent to its coefficient sequence being holonomic. It is well known
that all algebraic power series are holonomic. We show that the analogous
statement for sequences is false by proving that the sequence $\{\sqrt{n}\}_n$ is not holonomic.
In addition, we show that $\{n^n\}_n$, the Lambert $W$ function and $\{\log{n}\}_n$ are not holonomic,
where in the case of $\{\log{n}\}_n$ we have to rely on an open conjecture from transcendental number theory.},

journal = {Electronic Journal of Combinatorics},

volume = {11},

number = {1},

pages = {1--8},

isbn_issn = {ISSN 1077-8926},

year = {2004},

month = {12},

refereed = {yes},

institution = {RISC, J. Kepler University Linz},

length = {8},

url = {http://www.combinatorics.org/Volume_11/PDF/v11i1r87.pdf}

}