DataFrame rolling with complex function

Below is my quasi-code:

import pandas as pd

dict = {'a': [1,2,3,4,5,6,7,8], 
'b': [2,3,4,5,6,7,8,9], 
'c': [3,4,5,6,7,8,9,10]
}
df = pd.DataFrame.from_dict(dict)

def make_coeff(x):
    a_new = x[0]
    b_new = x[1]
    c_new = x[2]
    
    a_new.insert(0,1)
    b_new[0] = 1
    c_new[0] = 1
    
    return array_value(a_new, b_new, c_new)
    
df['array_col'] = df.rolling(3)[['a','b','c']].apply(make_coeff)

I want to create new col array_col depending on the rolling window with following actions:

insert 1 to a at beginning; change b[0] = c[0] = 1

use row 2 as an example:

row 2: a = [3,2,1], b = [4,3,2], c = [5,4,3] # 3 rolling window from row 2

row 2: a_new = [1,3,2,1], b_new = [1,3,2], c_new = [1,4,3] # action on each column

row 2 of array_col: array_value(a_new, b_new, c_new) # return a array value

here array_value is a known function returning an multi-dimensional array value. Let's assume it is a tensor product between all vectors with shape (len(a), len(b), len(c)):

def array_value(a, b ,c):
    tem = np.tensordot(a,b, axis=0)
    tem = np.tensordot(tem,c, axis=0)
    
    return tem

import pandas as pd
import numpy as np

dict = {'a': [1,2,3,4,5,6,7,8], 
'b': [2,3,4,5,6,7,8,9], 
'c': [3,4,5,6,7,8,9,10]
}
df = pd.DataFrame.from_dict(dict)


# create an array column of the rolling values of column a
df['a_rolling'] = [window.to_list() for window in df['a'].rolling(window=3)]
df['b_rolling'] = [window.to_list() for window in df['b'].rolling(window=3)]
df['c_rolling'] = [window.to_list() for window in df['c'].rolling(window=3)]

def make_coeff(a, b, c):
    if len(a) < 3:
        return [0,0,0] # the first couple of rows obviously don't have enough values
    # insert 0,1 at the beginning of a
    a = np.insert(a, 0, 0)
    b[0] = 1
    c[0] = 1
    
    return array_value(a, b, c)

def array_value(a, b ,c):
    tem = np.tensordot(a, b, axes=0)
    tem = np.tensordot(tem, c, axes=0)
    
    return tem

df['coeff'] = df.apply(lambda x: make_coeff(x['a_rolling'], x['b_rolling'], x['c_rolling']), axis=1)

This is likely not precisely what you want, but it is something