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Well it's me, Marko Riedel. ;-)

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2d
revised Exact result of a series using Euler-Maclaurin expansion.
correct mistake
2d
revised Weighted sum of cosines
correct mistake
2d
comment Weighted sum of cosines
@IgorRivin I solved the case $\alpha=-4.$ Enjoy.
2d
answered Weighted sum of cosines
2d
comment Weighted sum of cosines
@IgorRivin I can't tell until I actually do the calculation, but I would think yes, because a non-integral $\alpha$ will jam the works of the residue calculation in particular the cancellation. I might do $\alpha=-5$ because in fact it would interest me how it goes but I cannot be sure I will get around to it today.
2d
comment Weighted sum of cosines
You may want to consult this MSE link to see how your sum can be evaluated for $\alpha<-1$ a negative integer.
2d
comment Using a recursion tree to obtain an algorithm classification with n^2 time
The following MSE link may be useful reading and can easily be adapted to your question, keeping in mind that the relation between work term and recursive term is different, but the method goes through the same.
Oct
22
revised Average order of Eulers totient function squared
source of residue
Oct
21
revised Generate all permutations of a string containing repeated characters
simplify
Oct
21
revised Generate all permutations of a string containing repeated characters
no hash tables
Oct
21
revised Generate all permutations of a string containing repeated characters
set usage
Oct
21
answered Generate all permutations of a string containing repeated characters
Oct
21
answered Average order of Eulers totient function squared
Oct
20
comment Simple equivalent of the rest of the series $\sum\limits_n\frac1{n^3}$
The technique from this MSE link is easily adapted to this problem.
Oct
20
revised Black and white beads on a circle
semicolon
Oct
19
revised Expected number of returns to zero in a symmetric random walk - closed form
more explanatory material
Oct
19
revised Expected number of returns to zero in a symmetric random walk - closed form
terminology
Oct
19
comment Expected number of returns to zero in a symmetric random walk - closed form
Thanks. I added a line that shows the use of the coefficient extraction operator $[z^n]$ for power series.
Oct
19
revised Expected number of returns to zero in a symmetric random walk - closed form
intermediate step
Oct
19
revised Black and white beads on a circle
final version