Catalan numbers: Difference between revisions

Line 1:

{{wikipedia}}{{task|Arithmetic operations}}~~Catalan numbers are a sequence of numbers which can be defined directly:~~

⚫

:<math>C_n = \frac{1}{n+1}{2n\choose n} = \frac{(2n)!}{(n+1)!\,n!} \qquad\mbox{ for }n\ge 0.</math>

<br>

Catalan numbers are a sequence of numbers which can be defined directly:

⚫

::: <math> C_n = \frac{1}{n+1}{2n\choose n} = \frac{(2n)!}{(n+1)!\,n!} \qquad\mbox{ for }n\ge 0 </math>

</big></big>

Or recursively:

:<math>C_0 = 1 \quad \mbox{and} \quad C_{n+1}=\sum_{i=0}^{n}C_i\,C_{n-i}\quad\text{for }n\ge 0;</math>

::: <math> C_0 = 1 \quad \mbox{and} \quad C_{n+1}=\sum_{i=0}^{n}C_i\,C_{n-i}\quad\text{for }n\ge 0 </math>

</big></big>

Or alternatively (also recursive):

:<math>C_0 = 1 \quad \mbox{and} \quad C_n=\frac{2(2n-1)}{n+1}C_{n-1},</math>

::: <math> C_0 = 1 \quad \mbox{and} \quad C_n=\frac{2(2n-1)}{n+1}C_{n-1} </math>

</big></big>

;Task:

⚫

Implement at least one of these algorithms and print out the first 15 Catalan numbers with each.

[[Memoization]]   is not required, but may be worth the effort when using the second method above.

⚫

Implement at least one of these algorithms and print out the first 15 Catalan numbers with each. ~~[[Memoization]] is not required, but may be worth the effort when using the second method above.~~

Related tasks:

;Related tasks:

*[[Catalan numbers/Pascal's triangle]]

*[[Evaluate binomial coefficients]]

=={{header|360 Assembly}}==