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1d
revised Can you prove this identity involving the divisor sum function?
explain
1d
revised Can you prove this identity involving the divisor sum function?
language
1d
answered Can you prove this identity involving the divisor sum function?
1d
comment Number of ways to partition $40$ balls with $4$ colors into $4$ baskets
Thank your for verifying. I recently verified the generating function for several more terms than what the OEIS has.
1d
revised Number of ways to partition $40$ balls with $4$ colors into $4$ baskets
gf confirmed
1d
comment Solve the recurrence $T(n) = 2T(n/2) + n/\log n$
This recurrence also appeared at this MSE link.
2d
awarded  sequences-and-series
2d
comment # of partitions of $n$ into at most $r$ positive integers $=$ # of partitions of $n + r$ into exactly $r$ positive integers?
This problem also appeared at this MSE link:
Feb
7
comment Number of ways to partition $40$ balls with $4$ colors into $4$ baskets
Consult my post above which unfortunately tests the limits of the resources available on my machine (memory allocation). Signing off for the day.
Feb
7
revised Number of ways to partition $40$ balls with $4$ colors into $4$ baskets
general case
Feb
7
comment Number of ways to partition $40$ balls with $4$ colors into $4$ baskets
Very good indeed. Can you break up this formula over multiple lines using exponent minus one instead of the fraction? This way it does not break the vertical alignment on the page. Would you be interested in seeing some code for the computation of the case of five or six colors to see if you can spot the generating function?
Feb
6
revised Number of ways to partition $40$ balls with $4$ colors into $4$ baskets
addendum
Feb
6
revised Number of ways to partition $40$ balls with $4$ colors into $4$ baskets
clarify
Feb
6
answered Number of ways to partition $40$ balls with $4$ colors into $4$ baskets
Feb
5
comment Given the set $A=\{1,2,\dotsc,14\}$, find all subsets of $7$ elements that sum to a multiple of $7$.
The program posted at this MSE link will produce the answer $492.$
Feb
3
comment How many numbers of $10$ digits that have at least $5$ different digits are there?
Thanks! It so happens I was working on the same approach at this very moment! Please do have a look.
Feb
3
revised How many numbers of $10$ digits that have at least $5$ different digits are there?
closed form
Feb
3
revised How many numbers of $10$ digits that have at least $5$ different digits are there?
simplify
Feb
2
revised How many numbers of $10$ digits that have at least $5$ different digits are there?
clarify
Feb
2
revised How many numbers of $10$ digits that have at least $5$ different digits are there?
wording