How to compute cumulative sum of previous N rows in pandas?

Check the pandas.Series.expanding. The series.expanding(min_periods=2).sum()

will do the job for you. And don't forget to set 0-th element, since it is NaN. I mean,

accumulation = series.expanding(min_periods=2).sum()
accumulation[0] = series[0] # or as you like

you might have to do it the hard way

B = []
i =0
m_lim = 11
while i<len(A):
    if i<m_lim:
      B.append(sum(A[0:i]))
    if i>=m_lim and i < len(A) -m_lim:
        B.append(sum(A[i-m_lim:i]))
    if i>= len(A) -m_lim:
      B.append(sum(A[i:]))
    i=i+1
df['B'] = B

Call rolling with min_periods=1 and window=11 and sum:

In [142]:
df['A'].rolling(min_periods=1, window=11).sum()

Out[142]:
0       NaN
1      0.00
2      0.00
3      3.33
4     13.54
5     20.21
6     27.21
7     35.48
8     41.55
9     43.72
10    47.10
11    49.58
12    51.66
13    58.61
14    55.28
15    46.82
16    46.81
17    49.50
18    47.96
19    48.09
20    48.93
21    45.87
22    43.91
Name: A, dtype: float64