I want to define a recurrence relation $a(n)$ which is only defined for odd n.
I tried something like: a:= (2*n-1)->a(2n-3)+(2n-2)!+a(2n-5);
which apparently doesn't work.
How do I define this properly?
I'll post this here because it's too much for a comment. If you use the function...
You have a recurrence relation defined on all integers. Is it important that your relation remains undefined for even integers?
If you try to evaluate "a(2*n-1);" Maple will complain about too many levels of recursion. This is because it needs base cases. Since the recursion is 4th order, we'll need 4 initial conditions.
If you want it to be arbitrary, you can use...
Now if you ask Maple about a(5), a(7), etc., it will unwind the recurrence. However, if you ask for a(n), it'll complain about recursion again.
What are you trying to do? Maybe a function isn't the right tool.