Question: Summation , using two variables

I have the equation to calculate the legendre functions , but i am trying to find a way to form a loop so it would be less time consuming to find for a series of values.

Pn = sum((-1)^i*factorial(2*n-2*i)*x^(n-2*i)/(2^n*factorial(i)*factorial(n-i)*factorial(n-2*i)), i = 0 .. (1/2)*n)


This is the general equation , as you can see there are different values of P like p0,p1,p2,p3...depending on value of n .I can find each value by substituting n in the equation but it gets time consuming for higher values of n.So i would like to know if there is a way to form a loop so i could calculate the values of P for various values of n without having to do it each time individually.

As you can see from the worksheet , i can calculate Pn for n=1 by replacing n in the equation n sum it .But i want to automate it .

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