In[51]:= Array[BellNumber, 25]

Out[51]= {1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, \
4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, \
682076806159, 5832742205057, 51724158235372, 474869816156751, \
4506715738447323, 44152005855084346, 445958869294805289}

In[52]:= BellTriangle[10]

Out[52]= {{1}, {1, 2}, {2, 3, 5}, {5, 7, 10, 15}, {15, 20, 27, 37,
  52}, {52, 67, 87, 114, 151, 203}, {203, 255, 322, 409, 523, 674,
  877}, {877, 1080, 1335, 1657, 2066, 2589, 3263, 4140}, {4140, 5017,
  6097, 7432, 9089, 11155, 13744, 17007, 21147}, {21147, 25287, 30304,
   36401, 43833, 52922, 64077, 77821, 94828, 115975}}