Hi everyone,

In last educational round, I've stumbled upon a sequence as follows: 0,4,84,144,24. As it later turned out, this sequence (sometimes refered to as triangle read by rows, T(n,k)) was rather important, and not so easy to compute (for me, it required modular inversion for big numbers). It's in connection with Stirling numbers of the 2nd kind (i've included an image of the formula), and it got me thinking: aside from very basic sequences (like Catalan numbers, binomials or Fibonnacci), what enumerative combinatorical task solutions and ideas (of any difficulty) are must-known for competitive programming?

Marci