Hello I am trying to figure out how to correctly input this formula to find any number of coefficients I would like but somewhere along the way I seem to run into trouble. Could anyone tell me where I am going wrong? I thought using the RSolve function would easily solve this for me but all it gives me back is what I put in.

This is the format I am using, but it won't give me anything meaningful output:

RSolve[{a[n] == (n!/(\[Lambda] - \[Lambda]^n))*
    Sum[(a[n - k]*\[Lambda]^(n - k)*(-1)^k)/(k!*(n - 2 k)!), {k, 1, 
      Floor[n/2]}], a[n] == 1}, a[n], n]

Note that a[1]=1.