Expected number of packs to complete an album (linear)

recurrence.py

import math
  
evalue = [0] * 181
norm = math.comb(180, 4)

for i in range(1, 181):
  ans =  math.comb(i, 0) * math.comb(180 - i, 4 - 0) / norm
  for k in range(1, 5):
    if i - k >= 0:
      px = math.comb(i, k) * math.comb(180 - i, 4 - k) / norm
      ans += px * (1 + evalue[i - k])
  ans /= 1 - math.comb(180 - i, 4) / norm
  evalue[i] = ans
  print(i, evalue[i])