# Formulae for inversion of sequences?

David W. Cantrell DWCantrell at sigmaxi.org
Thu Oct 30 06:56:15 CET 2003

```Dear seqfan group:

In certain entries, would it be desirable to include a formula for
inverting the sequence? This question was brought to mind today
when a poster to sci.math asked, in essence, for the inverse of
A000984.
<http://www.research.att.com/projects/OEIS?Anum=A000984>
In other words, given m = C(2n, n), he wanted a formula for the
inverse function f, so that f(m) = n.

My answer, BTW, was essentially that,
letting q denote -Log(Log(16)/(m^2*Pi)),
the desired inverse function can be expressed as

Ceiling( (q + Log(q)) / Log(16) )

In other words, if m = C(2n, n) for integer n >= 0, then the above
expression yields n. Should this formula be included in the entry for
A000984? It certainly isn't an "obvious" formula, so perhaps it
should be included. But I question its utility, etc.

More importantly, in general, when would it be desirable to include
inversion formulae?

David Cantrell

```