0
$\begingroup$

Find an (approximate) closed-form solution for $S(m, b)$.

$$S(m,b)=\sum_{i=0}^{\lfloor (e-1)/2\rfloor}{e \choose i}S(m-1, b-i) \quad + \sum_{i=\lfloor (e-1)/2\rfloor+1}^{\min(b,e)}{e\choose i}{(m-1)e\choose b-i}$$

Improve this question
$\endgroup$
3
  • 3
    $\begingroup$ Needs some motivation or reason anyone should care about it. Perhaps some interpretation involving a random walk or ??. $\endgroup$
    – Gerald Edgar
    Commented May 15, 2013 at 15:51
  • $\begingroup$ Is this maybe some type of Eulerian numbers? $\endgroup$
    – Per Alexandersson
    Commented May 15, 2013 at 16:00
  • $\begingroup$ @Gerald, there might be a connection with the OP's other question, mathoverflow.net/questions/130115/probability-calculation -- but if so, it would be nice to make it more explicit. $\endgroup$
    – Barry Cipra
    Commented May 15, 2013 at 23:24

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .