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18h
comment How to calculate the sum $\sum_{i=0}^\infty i^nx^i$
This question recently appeared at this MSE link.
1d
comment Prove summations are equal
This was discussed at the following MSE link, which in fact points to two threads on this problem.
1d
answered How to prove this complex binomial power series identity?
1d
comment Circular arrangements of identical objects
There are a number of examples of this type of necklace and bracelet at this MSE Meta link.
2d
revised How to find a function that is the upper bound of this sum?
golden ratio
2d
revised How to find a function that is the upper bound of this sum?
constant II
2d
revised How to find a function that is the upper bound of this sum?
constant and linkage
2d
answered How to find a function that is the upper bound of this sum?
2d
comment Polya theorem and necklaces
The following list at MSE meta could prove useful reading.
2d
comment Multiplication partitioning into k distinct elements
The factorization is not a determining factor here, rather it is the coefficient extraction from the $5604$ terms in the cycle index $Z(P_{30})$. Fine-tuning this would appear to be a thesis type project involving a considerable effort of optimization and innovative coding.
Apr
25
revised Multiplication partitioning into k distinct elements
fix typo
Apr
25
revised Multiplication partitioning into k distinct elements
grammar
Apr
24
comment Multiplication partitioning into k distinct elements
I will certainly upvote a functional contribution in another language that would then confirm the results from the above post assuming I have not made any mistakes.
Apr
24
comment Multiplication partitioning into k distinct elements
Being a Linux user and programmer I strongly encourage translating these MAPLE routines for PET computations and making them available for anyone to use. (The link has contributions from a number of users.)
Apr
24
revised Multiplication partitioning into k distinct elements
comparison with brute-force
Apr
24
revised Multiplication partitioning into k distinct elements
pointer
Apr
24
revised Multiplication partitioning into k distinct elements
distinct factors, code
Apr
24
revised Multiplication partitioning into k distinct elements
distinct factors
Apr
24
answered Multiplication partitioning into k distinct elements
Apr
23
comment Compute the sum $\sum_{k=1}^{\infty}k^mz^k$ where $|z|<1$
I guess it will surprise no one that I prefer using the species equation as documented below. ;-) Unfortunately I lost a few minutes on the contour integral.