1, 2, 4, 8, 16, ... 33?
Python, 51 bytes



f=lambda n,k=2:n&lt;3or k&lt;n and f(k)*f(n-k-2)+f(n,k+1)


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Simplifies the formula a bit:

$$a(n) =  \sum_{k=2}^{n-1} a(k)\cdot a(n-2-k)$$

$$ a(-1) = a(0)= a(1)= a(2) = 1$$