@MISC{STIRL2_1.MIZ,
  AUTHOR = {P\c{a}k, Karol},
  TITLE = {Stirling Numbers of the Second Kind},
  DAY = {15},
  MONTH = {March},
  YEAR = {2005},
  ADDRESS1 = {University of Bialystok, ul. Akademicka 2, 15-267 Bialystok},
  SUMMARY = {In this paper we define Stirling numbers of the second kind
  by cardinality of certain functional classes such that
  $$S(n,k) = \{f {\rm ~where~} f
    {\rm~is~function~of~}n,k : f {\rm ~is~onto~"increasing} \}$$
  After that we show basic properties of this number in order
  to prove recursive dependence of Stirling number of the second kind.
  Next theorems are introduced to prove formula
  $$S(n,k) = \frac{1}{k!} \mathop\Sigma_{i=0}^{k-1}(-1)^i
  {{k}\choose{i}}(k-i)^n$$ where $k\leq n.$}}

