FindGeneratingFunction[{1, 2/3, 1/3, 4/27, 5/81, 2/81, 7/729, 8/2187, 1/729, 10/19683, 11/59049}, x]

]]>But you can try to get the gf using M.

]]>Let us see what else can be done.

We see powers of 3 in the denominator and remember that the generating function

has that property.

How did you find that gf?

]]>I particularly liked Borcherds's proof of Jacobi's triple product identity. Very elegant!

]]>I think I might post a similar thing (or two), but maybe in Euler's Avenue; it's not really Computer Math. I had a Descrete Mathematics course this semester, and the prof showed us some very cool proofs involving partitions, mostly combinatorial!

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