# Summation of Catalan Convolution

an someone help me solve this.
$\sum _{k=0}^{\infty } \frac{2^{-2-2 k} \binom{3+2 k}{k}}{4+k}$
Wolfram alpha says it converges to 1 , but actually I have no idea, how to solve it.

• The number 4 in the numerator sounds a little suspicious. Could you please double check and make sure that there is no typo?

• It is just multiplying, I will change it to be less vague.

• This looks much better.

• This is unlike any sequence I have seen before. How did you come up with this problem? Any motivation behind it?