all sequence solver

import math
import random

# Functions: difference(arrayin), findDifference(arrayin, differenceLevel), findTerm(difference, number), makeNewArray(arrayin, length), compare(array1, array2)

def difference(arrayin):
    # Accept array and output differences
    if Working:
        print("difference(" + str(arrayin) + ")")
    arrayout = []
    for i in range(len(arrayin)-1):
        arrayout.append(arrayin[i+1]-arrayin[i])
    if Working:
        print("return: " + str(arrayout))
    return arrayout

def findDifference(arrayin, differenceLevel):
    # Accept array and difference level
    # Return first number of resulting difference
    if Working:
        print("findDifference(" + str(arrayin) + ", " + str(differenceLevel) + ")")
    newDifference = arrayin
    for i in range(differenceLevel):
        newDifference = difference(newDifference)
    if Working:
        print("return: " + str(newDifference[0]))
    return newDifference[0]


def findTerm(difference, number):
    # Accept difference and number and return term
    if Working:
        print("findTerm(" + str(difference) + ", " + str(number) + ")")
    if Working:
        print("return: " + str(number / math.factorial(difference)))
    return number / math.factorial(difference)

def makeNewArray(arrayin, length):
    # Accept nth term in form of array (e.g 2x^2+3x+1 = [2, 3, 1]) and desired length of output and return sequence with given length
    if Working:
        print("makeNewArray(" + str(arrayin) + ", " + str(length) + ")")
    # 2x^2 + 3x + 1
    arrayout = []
    for j in range(1, length+1):
        add = 0
        for i in range(0, len(arrayin)):
            add += arrayin[i] * (j ** (len(arrayin)-i-1))
        arrayout.append(add)
    if Working:
        print("return: " + str(arrayout))
    return arrayout

def compare(array1, array2):
    # Accept array1 and array2 and return array1-array2 as an array
    # This assumes both are equal length
    if Working:
        print("compare(" + str(array1) + ", " + str(array2) + ")")
    array3 = []
    for i in range(len(array1)):
        array3.append(array1[i]-array2[i])
    if Working:
        print("return: " + str(array3))
    return array3

# -------------------------------------------------- #
# Note: after 16 or so inputted numbers, Python's precision starts to fall apart
# anything less than that might give you answers like 4.000000000232831 or -2.9999999331776053, just round those to 4 and -3 respectively.

Working = True
inp = [1, 18 ,22] # Input number sequence here
output = [0] * len(inp)
currentArray = inp
for currentTerm in range(len(inp)-1, -1, -1):
    currentDifference = findDifference(currentArray, currentTerm)
    term = findTerm(currentTerm, currentDifference)
    output[len(inp)-currentTerm-1] = term
    currentArray = makeNewArray(output, len(inp))
    currentArray = compare(inp, currentArray)

if Working:
    verification = makeNewArray(output, len(inp))
    print("##########\nRaw answer array:")
    print(output)
    print("##########\nInput sequence:")
    print(inp)
    print("#########\nOutput sequence:")
    print(verification)
print("##########\nnth term:")
for i in range(len(output)):
    print(str(output[i]) + "*n^" + str(len(inp)-(i+1)) + " + ", end="")