"""
Python module for OEIS sequence number A000166.

Examples of use.
----------------------------------------------------------------
>>> from a000166 import *
>>> print a000166_list(6)
[1, 0, 1, 2, 9, 44]
>>> for x in a000166_list_pairs(6):
...     print x
...
(0, 1)
(1, 0)
(2, 1)
(3, 2)
(4, 9)
(5, 44)
>>> print a000166_list_upto(10**6)
[1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496]
>>> print a000166(5)
44
----------------------------------------------------------------
"""

from itertools import islice, takewhile

__author__ = 'Nick Hobson <nickh@qbyte.org>'

def a000166_gen():
    """Generator function for OEIS sequence A000166.

    Uses the recurrence equation a(0)=1; a(n)=na(n-1) + (-1)^n, for n > 0.

    """
    x, n = 1, 0
    yield x
    while True:
        n += 1
        x = n*x + (-1)**n
        yield x

def a000166_list(n):
    """Returns a list of the first n >= 0 terms."""
    return list(islice(a000166_gen(), n))

def a000166_list_pairs(n):
    """Returns a list of tuples (n, a(n)) of the first n >= 0 terms."""
    return list(enumerate(islice(a000166_gen(), n)))

def a000166_list_upto(m):
    """Returns a list of all terms not exceeding m > 0."""
    return list(takewhile(lambda t: t <= m, a000166_gen()))

def a000166(n):
    """Returns the term with index n >= 0; offset 0."""
    return list(islice(a000166_gen(), n, n+1)).pop()