Recurrence relation here: $$ L(n) = \sum_{i=2}^n L(i-2)L(n-i),\,\, L(0)=1 $$
2026-04-17 17:06:55.1776445615
Any hint/idea of solving this recurrence relation?
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HINT
You may wish to consider the Catalan Numbers, which satisfy the following recurrence relation. $$ C_{n+1}=\sum_{i=0}^{n}C_i\,C_{n-i}\quad\text{for }n\ge 0$$ As provided here. Now what relation does the Catalan Numbers has to your recurrence relation?