Maxima: How to type a term of a complicated series

Question

How do you type the following general term of a series in Maxima ?

http://www.texify.com/img/%5CLARGE%5C%21u_%7Ba%7D%5E%7Bm%2Cn%7D%28h%29%3A%3D%28-h%29%5E%7Bn-a%7D%5Csum_%7Bj%3D0%7D%5E%7Bm-n%7D%28-1%29%5Ej%5C%28%5Carray%7Ba-n%5C%5C%5Cvspace%7B3%7D%5C%5Cn%7D%5C%29%281%2Bh%29%5Ej.gif

Answer 1

Well, first the binomial can be taken outside the sum and the sum can be performed in closed form:

Anyway, the entire expression you gave is entered into maxima as

u(a, m, n) := (-h)^(n-a) * sum((-1)^j * binomial(a-n,n) * (1+h)^j, j, 0, m-n);