Some new formulas for $π$

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We show how to find series expansions for $π$ of the form $π=\sum_{n=0}^\infty {S(n)}\big/{\binom{mn}{pn}a^n}$, where S(n) is some polynomial in $n$ (depending on $m,p,a$). We prove that there exist such expansions for $m=8k$, $p=4k$, $a=(-4)^k$, for any $k$, and give explicit examples for such expansions for small values of $m$, $p$ and $a$.
28 pages, LaTeX; some important references added

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