i was watching a video to learn about dynamic programming and in this video, the guy is using an interesting programming puzzle to help illustrate the concept of memoization.

the puzzle is really simple actually, it asks how many different ways you can travel a m by n grid if you're only allowed to go right or down.

anyways, i noticed that the answers followed a specific pattern and sure enough, when i input some of the answers into wolframalpha, it spit out equations which clearly follow some sort of pattern.

(pic related)

so i tried to "generalize" the solution by figuring out the pattern between the various equations but i'm stuck now.

can you help me? in the picture, the left most digit would be m and the equation after the -> is what wolframalpha spit out after i input all the results of n from 0 to 10.

the ? numbers below are from https://oeis.org/. 2 11 35 85 for example matches this series https://oeis.org/A000914

thank you for your time