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Huh, this is an interesting one. In principle, it should work, but your sum is so big (not long, just complicated) that it doesn't expand.

sage: h(1)
(-e^(-33/1024*k) + 1)^k - sum(((e^(33/1024*k*x) - 1)*e^(-33/1024*k*x))^k, x, 2, 15)
sage: sum(((e^(33/1024*k*x) - 1)*e^(-33/1024*k*x))^k, x, 2, 15)
((e^(33/512*k) - 1)*e^(-33/512*k))^k + ((e^(99/1024*k) - 1)*e^(-99/1024*k))^k + ((e^(33/256*k) - 1)*e^(-33/256*k))^k + ((e^(165/1024*k) - 1)*e^(-165/1024*k))^k + ((e^(99/512*k) - 1)*e^(-99/512*k))^k + ((e^(231/1024*k) - 1)*e^(-231/1024*k))^k + ((e^(33/128*k) - 1)*e^(-33/128*k))^k + ((e^(297/1024*k) - 1)*e^(-297/1024*k))^k + ((e^(165/512*k) - 1)*e^(-165/512*k))^k + ((e^(363/1024*k) - 1)*e^(-363/1024*k))^k + ((e^(99/256*k) - 1)*e^(-99/256*k))^k + ((e^(429/1024*k) - 1)*e^(-429/1024*k))^k + ((e^(231/512*k) - 1)*e^(-231/512*k))^k + ((e^(495/1024*k) - 1)*e^(-495/1024*k))^k

This is another manifestation of this question, I think, and ultimately I think it leads to Trac 9424.

But you want a workaround, presumably. From that ticket, we can try:

plot([SR(maxima_calculus(h(l)).simplify_sum()) for l in range(1,15)], (k,10,15))

This seems to work.