cp's OEIS Frontend

This sequence was chosen to illustrate a method of solution.

In general, for the expansion of 1/((1-t*x)^2*(1-s*x)*(1-r*x)) with r>s>t we have the formula: a(n) = ( K*r^(n+3) + L*s^(n+3) + M*t^(n+3) + N*t^(n+3) )/D where K,L,M,N,D have the following values:

K = (s-t)^2;

L = -(r-t)^2;

M = (r-s)*(r+s-2*t);

N = (r-t)*(s-t)*(r-s)*(n+3);

D = (r-s)*(r-t)^2*(s-t)^2.

Directly using formula we get a(n) = ( 4^(n+3) - 9*2^(n+3) + 8 + 6*(n+3) )/18. After transformation we obtain previous formula.