OEIS A280319 (Steinhaus–Johnson–Trotter algorithm)

# https://oeis.org/A280319
# listing the permutations generated by Steinhaus–Johnson–Trotter algorithm as their reverse colexicographic index numbers
# s_permutations comes from https://rosettacode.org/wiki/Permutations_by_swapping#Python:_recursive

from itertools import permutations
from bidict import bidict
from math import factorial


m = 7


sjt_numbers = []

for n in range(1, m+1):

    # generate n-element permutations in reverse colexicographic order
    perms_iter = permutations(list(range(n)))
    perms_revcolex_bidict = bidict()
    for i, perm in enumerate(perms_iter):
        perms_revcolex_bidict[factorial(n)-1-i] = tuple(perm[::-1])  # create reverse colexicographic order

    # generate n-element permutations in Steinhaus–Johnson–Trotter order
    def s_permutations(seq):
        def s_perm(seq):
            if not seq:
                return [[]]
            else:
                new_items = []
                for i, item in enumerate(s_perm(seq[:-1])):
                    if i % 2:
                        # step up
                        new_items += [item[:i] + seq[-1:] + item[i:]
                                      for i in range(len(item) + 1)]
                    else:
                        # step down
                        new_items += [item[:i] + seq[-1:] + item[i:]
                                      for i in range(len(item), -1, -1)]
                return new_items

        return [tuple(item) for item in s_perm(seq)]

    perms_sjt = s_permutations(list(range(n)))

    # assign rev colex index numbers to permutations
    for i in range(factorial(n)):
        perm = perms_sjt[i]
        sjt_number = perms_revcolex_bidict.inv[perm]
        sjt_numbers.append(sjt_number)


print(sjt_numbers)


b_file_text = ''

for i, e in enumerate(sjt_numbers):
    b_file_text += '%s %s\n' % (i, e)

b_file = open('b_file', 'w')
b_file.write(b_file_text)