I tried the following equation, Sum(i^4*Binomial(n,i),i,0,n), and MathStudio gave as solution the function: n*((2)^(n-4))*(n^3+3(n^2)+3n-2).
Substituting n=6 gave
1. Sum(i^4*Binomial(6,i),i,0,6), which returned 10752;
2. n=6, n*(2^(n-4))(n^3+3n^2+3*n-2), which returned 8160.
The number 10752 appears to be correct, and the correct formula for the function is n*(2^(n-4))(n^3+6n^2+3*n-2), substituting n=6 gives 10752.
Can anyone explain what I did wrong.