I'm unable to run the example as it segfaults on my computer because of the linear recursion but do you notice the same behavior with:

from time import time
from sys import setrecursionlimit

setrecursionlimit(10000000)

def recurse(i):
    if i < 0:
        return
    recurse(i-1)

if __name__ == '__main__':
    lo = 8
    hi = 16
    t = {}

    for sh in range(lo, hi):
        b4 = time()
        x = 1 << sh
        ret = recurse(x)
        after = time()
        t[sh] = after - b4

    for sh in range(lo+1, hi):
        print(t[sh] / t[sh-1])