After the code runs in half a minute now instead of a couple of days, it is time to examine the numerical stability:
y = y + x3 * xpow(c + i3);
Due to the accumulation, y and be larger than the 2nd part of the sum. This reduces the accuracy. It is better to accumulate the inner loop separately. In addition all terms of the sum are multiplied by x^3, so this can be done after the loop once:
Of course this changes the output slightly:
Now it is time to vectorize the inner loop:
function y = YourSum_vec(x, k)
y = y + sum(xpow(c:c + i1 + i2));
This reduces the runtime from 32.1 seconds to 20.8 seconds.
Compared to several days of the symbolic solution, this is both much faster. The vectorization was not the main part.