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Iterated functional composition

I try to translate a Maple function computing OEIS A144150 as given in [1]:

g := proc(p) local b; 
    b := proc(n) option remember; local k;
end end: 

A144150 := (n, k) -> (g@@k)(1)(n);


I am somewhat clueless how to achieve this with Sage. Google found [2] which highlights the problem but does not give an answer.