Combinatorial proof for Stirling number of 1st kind's generating function
54622
Stirling Numbers of the First Kind - a direct derivation
30414
Prove using combinatorics $\sum\limits_{k=0}^n 2^k \binom{n}{k} \binom{n-k}{\lfloor{\frac{n-k}{2}}\rfloor}=\binom{2n+1}{n}$
90957
Relation between Stirling numbers of first kind and harmonic numbers
61592
Exponential generating function to find recurrence formula $a_n$
146083
Stirling numbers of the second kind on Multiset
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
146867
Combinatorial Proof Of A Number Theory Theorem--Confusion
86389
Combinatorial argument to prove the recurrence relation for number of derangements
6366
Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
10917
Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
78314
Generating function for the factorial sequence
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
34299
Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
128971
Explicit formulas for Stirling numbers of second kind
152911
Stirling numbers combinatorial proof
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
142477
Closed-form expression for the number of $k$-permutations of length $n$. Duplicates allowed!