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a n|n<4=1|0<1=sum[an=max(sum[a k*a(n-2-k)|k<-[2..n-1]])1
Try it online!Try it online!
For n<3 the sum is 0, so max ... 1 raises it to 1.
n<3
sum
max ... 1
1
Edit: -6 bytes thanks to @Jo King.
a n|n<4=1|0<1=sum[a k*a(n-2-k)|k<-[2..n-1]]
Try it online!
a n=max(sum[a k*a(n-2-k)|k<-[2..n-1]])1
a n|n<4=1|m<-n-2=a(n-1)+sum[an|n<4=1|0<1=sum[a k*a(mn-2-k)|k<-[2..m]]n-1]]
A direct implementation of the recursive formulaEdit: -6 bytes thanks to @Jo King.
a n|n<4=1|m<-n-2=a(n-1)+sum[a k*a(m-k)|k<-[2..m]]
A direct implementation of the recursive formula.
