#! /usr/bin/env python
#
def subfactorial_values ( n_data ):

#*****************************************************************************80
#
## SUBFACTORIAL_VALUES returns values of the subfactorial function.
#
#  Discussion:
#
#    The subfactorial function Subfactorial(N) counts the number of 
#    permutations of N objects which leave no object unchanged.
#
#    Such a permutation is known as a derangement.
#
#    In Mathematica, the function can be evaluated by:
#
#      << DiscreteMath`CombinatorialFunctions`
#      Subfactorial[n]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz, Irene Stegun,
#    Handbook of Mathematical Functions,
#    National Bureau of Standards, 1964,
#    ISBN: 0-486-61272-4,
#    LC: QA47.A34.
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Cambridge University Press, 1999,
#    ISBN: 0-521-64314-7,
#    LC: QA76.95.W65.
#
#  Parameters:
#
#    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
#    first call.  On each call, the routine increments N_DATA by 1, and
#    returns the corresponding data; when there is no more data, the
#    output value of N_DATA will be 0 again.
#
#    Output, integer N, the argument of the function.
#
#    Output, integer F, the value of the function.
#
  import numpy as np

  n_max = 13

  f_vec = np.array ( ( \
            1, \
            0, \
            1, \
            2, \
            9, \
           44, \
          265, \
         1854, \
        14833, \
       133496, \
      1334961, \
     14684570, \
    176214841 ))

  n_vec = np.array ( ( \
     0,  1,  2,  3, \
     4,  5,  6,  7, \
     8,  9, 10, 11, \
    12 ))

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    n = 0
    f = 0
  else:
    n = n_vec[n_data]
    f = f_vec[n_data]
    n_data = n_data + 1

  return n_data, n, f

def subfactorial_values_test ( ):

#*****************************************************************************80
#
## SUBFACTORIAL_VALUES_TEST demonstrates the use of SUBFACTORIAL_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'SUBFACTORIAL_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  SUBFACTORIAL_VALUES stores values of the SUBFACTORIAL function.' )
  print ( '' )
  print ( '             N    Subfactorial(N)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, f = subfactorial_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12d  %12d' % ( n, f ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'SUBFACTORIAL_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  subfactorial_values_test ( )
  timestamp ( )