An Interesting combination problem

Правка en1, от Yubai, 2022-07-31 10:00:32

Try to solve the following problem, only by combining meaning but not the generating function.

$$$\sum_x \binom{2x+k}{x}\binom{P-2x-k}{a-x}$$$

There are q times inquiries, Given k, P, a, each time, print the value of this sum, $$$q,k,P,a \leq 1e5$$$.

I'll give an answer in 24 hours. If solved, please write the method in the comments and try the harder problems below, which replace 2 by t, t will be given before all queries.

$$$\sum_x \binom{tx+k}{x}\binom{P-tx-k}{a-x}$$$

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en1 Английский Yubai 2022-07-31 10:00:32 513 Initial revision (published)