Question: Borel-Tanner moments

For m=1,2, how do I show with Maple that the first two moments of the Borel-Tanner distribution are simple functions of k and lamda, e.g., k/(1-lambda) for the mean? How do I get the closed-form expressions with maple? Code:

simplify(sum(x^m*k*x^(x-k-1)*lambda^(x-k)*exp(-lambda*x)/factorial(x-k), x = k .. infinity)) assuming lambda > 0, lambda < 1, k::posint; evalf(subs(k = 1, lambda = .8, %))

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