Computing a large coefficient in a power series expansion

Question

What is the coefficient of $x^{1000}$ in the power series expansion of $$\frac{1}{(1-x)(1-x^5)(1-x^{10})(1-x^{25})}?$$

This is the number of ways to break ten dollars into pennies, nickels, dimes, and quarters.

I am especially interested in whether there is a nice way to do this kind of calculation in Sage, or in Wolfram Alpha.

Answer 1

Using Maple with the following command

coeff(convert(series(1/((1-x)*(1-x^5)*(1-x^10)*(1-x^25)),x=0,1200),polynom),x,1000);

we obtain $142511$.

A similar command will work with Sage or Maxima.

Answer 2

Take the partial fraction decomposition of the above fraction. Then collect terms.