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Catalan numbers: Difference between revisions
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shown the formulas in larger fonts to be easier to read the italics and subscripts, add a Task (bold) header.
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{{wikipedia}}{{task|Arithmetic operations}}
:<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:
<big><big>
▲::: <math> C_n = \frac{1}{n+1}{2n\choose n} = \frac{(2n)!}{(n+1)!\,n!} \qquad\mbox{ for }n\ge 0
</big></big>
Or recursively:
<big><big>
::: <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
</big></big>
Or alternatively (also recursive):
<big><big>
::: <math> C_0 = 1 \quad \mbox{and} \quad C_n=\frac{2(2n-1)}{n+1}C_{n-1}
</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:
*[[Catalan numbers/Pascal's triangle]]
*[[Evaluate binomial coefficients]]
<br><br>
=={{header|360 Assembly}}==
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