Intereting Posts

How many ways are there to position two black rooks and two white rooks on an 8X8 chessboard
How to remember a particular class of trig identities.
On commutative unital graded rings in which no element in any homogenous part has a zero divisor
Covariance of product of two functions of two binomial distributions
How to prove $3^\pi>\pi^3$ using algebra or geometry?
Solving Recurrence $T_n = T_{n-1}*T_{n-2} + T_{n-3}$
“Box With No Top” Optimization
Differentiation using first principles with rational powers
martingale and filtration
How to find B-Spline represenation of an Akima spline?
How to prove $\lim_{x\to \infty} {x \over \sin(x) + x} = 1$?
Evaluate the improper integral $ \int_0^1 \frac{\ln(1+x)}{x}\,dx $
Sum of two squares $n = a^2 + b^2$
Compute the trigonometric integrals
Does this series diverge: $(\sqrt 2-\sqrt 1)+(\sqrt 3-\sqrt 2)+(\sqrt 4-\sqrt 3)+(\sqrt 5-\sqrt 4)+\dots$?

How many ways are there to stack coins on top of the other (2D stack) without any coin falling down ?

Here’s an example for $n=3$:

- Catalan Numbers Staircase bijection
- How to deal with this double summation?
- Verifying Touchard's Identity
- Triangulations of n-gon
- Hard binomial sum
- Closed form for $ S(m) = \sum_{n=1}^\infty \frac{2^n \cdot n^m}{\binom{2n}n} $ for integer $m$?

Now this is most likely just like the monotonic path of Catalan number with up and down instead of up and right but I just don’t get why is that ? Well, any advice would be appreciated.

- In combinatorics, how can one verify that one has counted correctly?
- Number of bit strings with 3 consecutive zeros or 4 consecutive 1s
- An efficient method for computing the number of submultisets of size n, of a given multiset
- Number of possibilities for n persons at m tables with at least 5 persons per table
- Distributing 6 oranges, 1 apple, 1 banana and 1 pineapple among 3 children
- Is there a characterization of groups with the property $\forall N\unlhd G,\:\exists H\leq G\text{ s.t. }H\cong G/N$?
- Balls in bins, probability that exactly two bins are empty
- How to find all possible combinations of a set of options?
- A question on the Lagrange Inversion Formula
- Is there a name for this type of permutation?

A picture is worth a thousand words, they say:

- Proof for $A \cup B = B$ if and only if $A \subset B$
- Solving a recurrence relation, $a_n = \sqrt{n(n+1)}a_{n-1} + n!(n+1)^{3/2}$
- Bounded partial derivatives imply continuity
- Estimates on conjugacy classes of a finite group.
- Continued Fraction
- How to prove $\inf(S)=-\sup(-S)$?
- Prove $\int_0^{\infty} \left(\sqrt{1+x^{4}}-x^{2}\right)\ dx=\frac{\Gamma^{2}\left(\frac{1}{4}\right)}{6\sqrt{\pi}}$
- Extension of a Uniformly Continuous Function between Metric Spaces
- Proof that $(1+1/x)^x$ is monotonic increasing
- Local ring on generic fiber
- Additive basis of order n: Sets which allow every integer to be expressed as the sum of at most n members of that set.
- Why does casting out $9$ and $11$ work to compute remainders?
- A homotopy equivalence between spaces $B\Gamma$ and $K\Gamma$ for a graph of groups on a graph $\Gamma$
- Integrating the formula for the sum of the first $n$ natural numbers
- Generalizations of colorability