Getting Overflow error from lifetimes package

Question

Below is a sample of the dataset I am using as well as the bgmodel

The summary table was created from utilizing the below code

from lifetimes import BetaGeoFitter
from lifetimes.plotting import plot_period_transactions, plot_frequency_recency_matrix, plot_probability_alive_matrix, plot_history_alive

bgModel = BetaGeoFitter()
bgModel.fit(new_df['lifetime_orders'], new_df['days_last'], new_df['T'])

bgModel.summary

I am trying to get expected number of transactions a customer will do over a year, and the probability that the customer is still alive right now by utilzing the below code

def bgnbd_expectations(x, t_x, T, t):
    r, alpha, a, b = bgModel.summary.iloc[:,0]
    aa = r+x
    bb = b+x
    cc = a+b+x-1
    z = t/(t+alpha+T)
    terms = np.zeros(shape=(151))
    terms[0]=1
    for i in range(1,len(terms)):
        terms[i] = terms[i-1]*(aa+i-1)*(bb+i-1)/((cc+i-1)*i)*z
    f2_1 = sum(terms)
    if x > 0:
        rpos = 1
    else:
        rpos = 0
        
    eyt = ((a+b+x-1)/(a-1))*(1-(((alpha+T)/(alpha+T+t))**(r+x))*f2_1)/(1+(rpos*(a/(b+x-1)))*((alpha+T)/(alpha+t_x))**(r+x))
    
    prob = 1/(1+(rpos*(a/(b+x-1))*((alpha+T)/(alpha+t_x))**(r+x)))
    return eyt, prob

This portion of the code sets up the probablity alive and expected transacations once I run this code I follow it up with

alive = []
nextyear = []
for i, row in new_df.iterrows():
    ex, proAl = bgnbd_expectations(row.lifetime_orders, row.days_last, row.T, 52) #52 weeks in a year
    alive.append(proAl)
    nextyear.append(ex)
new_df['ProbabilityAlive'] = alive
new_df['ExpectedTransactions'] = nextyear
new_df.head()

To produce the output. HOWEVER for some reason the code either runs and the output is a long string that includes the column names from the sample dataset appended to the probability and expected transcation values or I get an Overflow error (OverflowError: (34, 'Result too large'))