MHB Coefficent in a infinite power series

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To find the coefficient of x^9 in an infinite power series, one can analyze the combinations of terms that sum to 9. The equation 9 = 0 + 9, 1 + 8, 2 + 7, and so on, illustrates the various combinations of non-negative integers that yield this result. Each combination corresponds to a unique product contributing to the coefficient. In total, there are 10 distinct products that result in x^9. Therefore, the coefficient of x^9 in the series is 10.
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How do I find a coefficent of x^9 in a power series like this:
Screenshot 2021-06-03 174217.png
 
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For (a) 9= 0+ 9= 1+8= 2+ 7= 3+ 6= 4+ 5= 5+ 4= 6+ 3= 7+ 2= 8+ 1= 9+ 0.
There are 10 products that give $x^9$ so the coefficient is 10.
 

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