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I've been solving a problem which forces me to answer the question: "Is there a boolean function with exponential number (in variable count) of prime implicants of the length n - 1?"

Anyway, during solving this problem I came to this point:

Is the following sum exponential in [itex]2n[/itex]?

[tex]

\sum_{x=0}^{n} \left( \begin{array}{cc} 2n \\ 2x \end{array} \right)

[/tex]

Are there some nice combinatorial identities which I overlooked that can be useful in this case?

Thank you very much.

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# Is this sum exponential?

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