Why does a function seem to be executed more times than the number of elements passed to np.vectorize(function)?

The function is called twice to determine the number of outputs.

numpy.vectorize documentation (Notes):

If neither otypes nor signature are specified, then a call to the function with the first argument will be used to determine the number of outputs. The results of this call will be cached if cache is True to prevent calling the function twice. However, to implement the cache, the original function must be wrapped which will slow down subsequent calls, so only do this if your function is expensive.

Specifying the type will prevent the second call:

print(np.vectorize(f, otypes=[object])(["input"]))

Setting cache to True:

print(np.vectorize(f, cache=True)(["input"]))

Those both output

hi input
['input']

You can also specify the signature:

print(np.vectorize(f, signature="(m)->(m)")(["input"]))

This will output

hi ['input']
['input']

Try it online!