(12C+) Bernoulli Number

[Albert Chan]

Python code for Bernoulli Number (also return the forward difference table)

Code:

from fractions import Fraction

def B_fdiff(n):
    lst = [1,1] + [i**n for i in range(2, n+2)]
    for i in range(n):
        for j in range(n,i,-1): lst[j+1] -= lst[j]  # forward diff
        lst[0] = Fraction(lst[i+2],i+2) - lst[0]    # B(n) value
    return lst

>>> B_fdiff(6)
[Fraction(1, 42), 1, 63, 602, 2100, 3360, 2520, 720]

>>> for i in range(13): print i, B_fdiff(i)[0]
...
0 1
1 -1/2
2 1/6
3 0
4 -1/30
5 0
6 1/42
7 0
8 -1/30
9 0
10 5/66
11 0
12 -691/2730