This turns out to be a much easier way to solve the problem. Let's denote Stirling numbers as calls of the function `s'.
First, we store the rewrite rules corresponding to the definition of Stirling numbers in a convenient variable:
s e StirlingRules RET [ s(n,n) := 1 :: n >= 0, s(n,0) := 0 :: n > 0, s(n,m) := s(n-1,m-1) - (n-1) s(n-1,m) :: n >= m :: m >= 1 ] C-c C-c
Now, it's just a matter of applying the rules:
2: 4 1: s(4, 2) 1: 11 1: 2 . . . 4 RET 2 C-x ( ' s($$,$) RET a r StirlingRules RET C-x )
As in the case of the
fib rules, it would be useful to put these
EvalRules and to add a `:: remember' condition to
the last rule.