On the Constant Terms of Certain Laurent Series

We study the divisibility properties of the constant terms of certain meromorphic modular forms for Hecke groups and relate those properties to several O.E.I.S. sequences and several other sequences, the members of which appear in congruences of Ramanujan. At the end of the article, we construct from elementary arithmetic functions some meromorphic but not necessarily modular functions and study their constant terms. For our use in subsequent drafts, we work out a variation of the multinomial theorem convenient for application to single-variable power series.