No answer for computing a sum?

Questions
1

Mathematica gives no answer what is the problem with the sum as is probably convergent

Sum[((-z)^k*Gamma[-k - n - \[Lambda], 0, -1])/(2^k*k!), {k, 0, 
  Infinity}]
2

What other result are you expecting? Not every sum has a known closed form.

3

Thanks