Background

I'm modeling Genetic Algorithm(GA) with Markov chains and deriving the expression for the expectation of the first hittig time in the MC with 1 absorbing state and $l-1$ transient states. This results is an expression for a sum involving square of a binomial coefficient

Problem I need to find a closed expression for $$\sum_{k=0}^{l/2} \binom{l/2}{k}^2 p^{2k}$$

where $p$ is a function of $l$ and lies between 0 and 1.

So far I've found a closed expression for $$\sum_{k=0}^{n}k^2 \binom{n}{k}^2$$

Any suggestions are very much appreciated.

pandl? – Thierry Zell Jan 23 '11 at 1:48