There is no useful closed-form for this. You can write it down as
$$2^N - \binomial{N}{k+1} {}2Fbinom{N}{k+1} {1}(1, }_2F_{1}(1, k+1-N, k+2; -1)$$
but that's really just a rewrite of the sum in a different form.
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There is no useful closed-form for this. You can write it down as $$2^N - \binomial{N}{k+1} {}2F{1}(1, k+1-N, k+2; -1)$$ but that's really just a rewrite of the sum in a different form. |
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