bell1:=proc(n)
  option remember;
  add(binomial(n-1,k)*bell1(k),k=0..n-1)
end:
bell1(0):=1:

bell1(50);
#        185724268771078270438257767181908917499221852770

combinat[bell](50);
#        185724268771078270438257767181908917499221852770

bell1~([$0..20]);
#  [1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570,
#    4213597, 27644437, 190899322, 1382958545, 10480142147,
#    82864869804, 682076806159, 5832742205057, 51724158235372]