This tag is for basic questions about the study of finite or countable discrete structures — specifically how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions. ...

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5
votes
0answers
94 views
+50

Number of ways to express a binary number in a certain way

So I'm working on a problem where I get to a point where I have to count the number of solutions to an equation or at least find a decent upper bound to be used in an estimate I need later. The ...
4
votes
2answers
117 views
+100

the first $2k$ terms of the power series of $\sec x + \tan x$ at $x=-\pi/2$

We know the power series of $\sec x+\tan x$ is as follows, $f(x)=\sum_{n\geq 0}\frac{E_n}{n!}x^n$, where $E_n$ is Euler Zigzag numbers and clearly the radius of convergence of $f(x)$ is $\pi/2$. ...
2
votes
0answers
50 views
+200

Generating Function for 2-Associated Stirling Numbers of the Second Kind

I am looking for a paper which explicitly defines a power series for 2-associated Stirling Numbers of the Second Kind. The paper defines the generating function as follows: Let $S_2(n,k)=b(n,k)$ be ...