17 lines
694 B
Python
17 lines
694 B
Python
|
def catalan_number(num):
|
|||
|
|
if num <=1:
|
|||
|
|
return 1
|
|||
|
|
|
|||
|
|
res_num = 0
|
|||
|
|
for i in range(num):
|
|||
|
|
res_num += catalan_number(i) * catalan_number(num-i-1)
|
|||
|
|
return res_num
|
|||
|
|
|
|||
|
|
for n in range(10):
|
|||
|
|
print(catalan_number(n))
|
|||
|
|
|
|||
|
|
# In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. They are named after the Belgian mathematician Eugène Charles Catalan (1814–1894).
|
|||
|
|
|
|||
|
|
Catalan number
|
|||
|
|
The first Catalan numbers for n = 0, 1, 2, 3, … are
|
|||
|
|
1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, ....
|