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In your last line, you use h to define h itself.

In your last line, you use h to define h itself.

sage: def hh(i):
....:     if i<1:
....:         return 0
....:     else:
....:         return hh(i-1) + g[i]
....:         
sage: h = [hh(i) for i in range(len(d)-1)]
sage: h
[0, 1, 2, 3, 4, 5, 6, 7]

sage: @cached_function
....: def hh(i):
....:     if i<1:
....:         return 0
....:     else:
....:         return hh(i-1) + g[i]
....:         
sage: h = [hh(i) for i in range(len(d)-1)]
sage: h
[0, 1, 2, 3, 4, 5, 6, 7]

In your last line, you use h to define h itself.

EDIT (given the explanation provided in comments): it is not possible to do such a thing. Indeed, when you write h=[...], the Python name h is created after the object [...] is created.

So, you have to define a recursive function as follows:

sage: def hh(i):
....:     if i<1:
....:         return 0
....:     else:
....:         return hh(i-1) + g[i]
....:         
sage: h = [hh(i) for i in range(len(d)-1)]
sage: h
[0, 1, 2, 3, 4, 5, 6, 7]

That said, i guess (i might be wrong in your motivation), that you wanted to use a list so that when you compute h[4], you do not have to do the whole recursion by computing h[3], h[2], h[1], h[0], which is what hh does. The trick is to use the @cached_function decorator, that ocmputes computes h[i] only once and memoizes the result for further calls. So, you can do:

sage: @cached_function
....: def hh(i):
....:     if i<1:
....:         return 0
....:     else:
....:         return hh(i-1) + g[i]
....:         
sage: h = [hh(i) for i in range(len(d)-1)]
sage: h
[0, 1, 2, 3, 4, 5, 6, 7]

In your last line, you use h to define h itself.

EDIT (given the explanation provided in comments): it is not possible to do such a thing. Indeed, when you write h=[...], the Python name h is created after the object [...] is created.

So, you have to define a recursive function as follows:

sage: def hh(i):
....:     if i<1:
....:         return 0
....:     else:
....:         return hh(i-1) + g[i]
....:         
sage: h = [hh(i) for i in range(len(d)-1)]
sage: h
[0, 1, 2, 3, 4, 5, 6, 7]

That said, i guess (i might be wrong in your motivation), that you wanted to use a list so that when you compute h[4], you do not have to do the whole recursion by computing h[3], h[2], h[1], h[0], again, which is what hh does. The trick is to use the @cached_function decorator, that computes h[i] only once and memoizes the result for further calls. So, you can do:

sage: @cached_function
....: def hh(i):
....:     if i<1:
....:         return 0
....:     else:
....:         return hh(i-1) + g[i]
....:         
sage: h = [hh(i) for i in range(len(d)-1)]
sage: h
[0, 1, 2, 3, 4, 5, 6, 7]