Consider the problem of stacking coins in the plane. Prove that the number of coin configurations satisfies the Catalan recurrence
125214
Catalan numbers - number of ways to stack coins
86397
throwing a $k$-sided dice until you get every face the same number of times
35648
How many permutations of the set n={1,2,3,3,3,4,4,5} are possible without any consecutive identical elements?
107964
Simple combinatorics problem.
130851
Squaring the plane, with consecutive integer squares. And a related arrangement
158925
How many sequences of $n$ tosses of a coin that do not contain two consecutive heads have tails as the first toss?
58508
Number of ways to pair off $2n$ points such that no chords intersect
43033
Proof on Catalan numbers
46469
$n$ Lines in the Plane
74730
Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
959
Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.
150281
Am I on the right track to figure out this combinatorics problem?
59873
Proof of clockwise towers of Hanoi variant recursive solution
44070
Recurrence  for number of regions formed by diagonals of a convex polygon.
9411
Number of permutations of $n$ elements where no number $i$ is in position $i$
31340
Concurrent lines proof for a regular 18-gon
56828
A combinatorial proof that the alternating sum of binomial coefficients is zero