OEIS A280318 (Heap's algorithm)

# https://oeis.org/A280318
# listing the permutations generated by Heap's algorithm as their reverse colexicographic index numbers
# _heap_perm_ comes from http://stackoverflow.com/questions/29042819/heaps-algorithm-permutation-generator

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


n = 7

# 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 Heap order
def _heap_perm_(n, A):
    if n == 1: yield A
    else:
        for i in range(n-1):
            for hp in _heap_perm_(n-1, A): yield hp
            j = 0 if (n % 2) == 1 else i
            A[j],A[n-1] = A[n-1],A[j]
        for hp in _heap_perm_(n-1, A): yield hp

heap_generator = _heap_perm_(n, list(range(n)))
perms_heap = {}
for i, perm in enumerate(heap_generator):
    perms_heap[i] = tuple(perm)

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


print(heap_numbers)

b_file_text = ''

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

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