Newbetuts

How to find the sum $\sum_{k=1}^{\lfloor n/2\rfloor}\frac{2^{n-2k}\binom{n-2}{2k-2}\binom{2k-2}{k-1}}{k}$

Non-crossing partitions without singletons

Showing Directly that Dyck Paths Satisfy the Catalan Recurrence

Dyck paths with $k$ peaks

Alternative proof of an intereting identity of Catalan's Numbers and central binomial coefficients

Catalan numbers and triangulations

Catalan numbers. Sequence of balanced parentheses.

Number of Dyck Paths Bounded by $M$

A recurrence for the number of non-crossing partitions without singletons, using Dyck paths

Identity with Harmonic and Catalan numbers

Explanation/Intuition behind why $C_n$ counts the number of triangulations of a convex $n+2$-gon?

Show that that $\lim_{n\to\infty}\sqrt[n]{\binom{2n}{n}} = 4$

Riordan numbers recurrence

How to prove $\sum_{s=0}^{m}{2s\choose s}{s\choose m-s}\frac{(-1)^s}{s+1}=(-1)^m$?

Find the generating function of $f(n) = \sum_{k = 0}^n \binom{n}{k} (-1)^{n-k}C_{k}$

Harmonic Numbers series I

New posts in catalan-numbers

Combinatorial Interpretation of Fractional Binomial Coefficients

Prove that $a_n$ is a perfect square if $n$ is even without generating functions or Taylor series.

Generating function and integer sequence that arise from this function

"Ballot numbers" sum up to Catalan numbers

How to find the sum $\sum_{k=1}^{\lfloor n/2\rfloor}\frac{2^{n-2k}\binom{n-2}{2k-2}\binom{2k-2}{k-1}}{k}$

Non-crossing partitions without singletons

Showing Directly that Dyck Paths Satisfy the Catalan Recurrence

Dyck paths with $k$ peaks

Alternative proof of an intereting identity of Catalan's Numbers and central binomial coefficients

Catalan numbers and triangulations

Catalan numbers. Sequence of balanced parentheses.

Number of Dyck Paths Bounded by $M$

A recurrence for the number of non-crossing partitions without singletons, using Dyck paths

Identity with Harmonic and Catalan numbers

Explanation/Intuition behind why $C_n$ counts the number of triangulations of a convex $n+2$-gon?

Show that that $\lim_{n\to\infty}\sqrt[n]{\binom{2n}{n}} = 4$

Riordan numbers recurrence

How to prove $\sum_{s=0}^{m}{2s\choose s}{s\choose m-s}\frac{(-1)^s}{s+1}=(-1)^m$?

Find the generating function of $f(n) = \sum_{k = 0}^n \binom{n}{k} (-1)^{n-k}C_{k}$

Harmonic Numbers series I