I am trying to write a little program (called "rcltnn") which calculates a recurrence. The problem: Maple does not return numbers but strings which arrise from the recurrence. Example: for n=4 I expect to get rcltnn(n=4)=95, but Maple gives
Actually, that string is correct but not fully evaluated.
We have rcltnn(2)=2 and rcltnn(3)=11 (further values are rcltnn(1)=1 and rcltnn(0)=0).
Here my program (I have played with many versions of this program)
rctlnn := proc (n::integer) global j, rctlnn; option remember; if n = 0 then rctlnn := 0 else rctlnn := combinat:-bell(n); for j from 2 to n-1 do rctlnn := rctlnn+combinat:-stirling2(n,j)*rcltnn(j) end do; end if end proc;
The command "eval" did not help in my attempts.
I want to study rctlnn(n) by Maple. It would be nice to find an explicit formula (not a recurrence) for rctlnn. Furthermore, does it make sense to try asympt(rctlnn,n) to get an asymptotic formula? Any hints will be appreciated!