Status: Valid
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 3510 by [email protected]: implement Stirling numbers
http://code.google.com/p/sympy/issues/detail?id=3510
The number of partitions of n items into k bins is given be the Stirling
number of the second kind. I see we have a wester test that tests for S1.
Perhaps both could be added.
http://en.wikipedia.org/wiki/Stirling_number_of_the_second_kind
def S2(n, k):
... if k > n:
... return 0
... j = Dummy()
... arg = (-1)**(k-j)*j**n*binomial(k,j)
... return 1/factorial(k)*Sum(arg,(j,0,k)).doit()
...
for n in range(11):
... for k in range(11):
... print S2(n,k),
... print
...
1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 0 0 0
0 1 3 1 0 0 0 0 0 0 0
0 1 7 6 1 0 0 0 0 0 0
0 1 15 25 10 1 0 0 0 0 0
0 1 31 90 65 15 1 0 0 0 0
0 1 63 301 350 140 21 1 0 0 0
0 1 127 966 1701 1050 266 28 1 0 0
0 1 255 3025 7770 6951 2646 462 36 1 0
0 1 511 9330 34105 42525 22827 5880 750 45 1
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