Comment #1 on issue 3510 by Franck.Dernoncourt: implement Stirling numbers
http://code.google.com/p/sympy/issues/detail?id=3510
You might want to use dynamic programming instead, which is by faster.
Computing n=k=100 takes forever using your code and is immediate (< 1
second) using dynamic programming.
(just an example quickly extracted from my code)
Code:
cache_size= 10
cache = [[0 for j in range(cache_size)] for i in range(cache_size)]
def generate_cache():
cache[0][0] = 1
for i in range(1, cache_size):
for j in range(1, cache_size):
cache[i][j]=cache[i-1][j-1] + j* cache[i-1][j]
def main():
generate_cache()
for i in range(0, cache_size):
print cache[i]
if __name__ == "__main__":
main()
Output:
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 1, 0, 0, 0, 0, 0, 0, 0]
[0, 1, 3, 1, 0, 0, 0, 0, 0, 0]
[0, 1, 7, 6, 1, 0, 0, 0, 0, 0]
[0, 1, 15, 25, 10, 1, 0, 0, 0, 0]
[0, 1, 31, 90, 65, 15, 1, 0, 0, 0]
[0, 1, 63, 301, 350, 140, 21, 1, 0, 0]
[0, 1, 127, 966, 1701, 1050, 266, 28, 1, 0]
[0, 1, 255, 3025, 7770, 6951, 2646, 462, 36, 1]
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