"The numbers C$($n$,$ k$)$ are defined for all n$,$ k $0$ by the following three rules: $$ C $($n$,0)=1$ C $($n$,$ k$)=0,$ if k $>$ n $$ C $($n$,$ k$)=$ C $($n$-1,$ k$)+$ C$($n$-1,$ k$-1),$ for n $$ k $>0.$ A recursive Python function that computes C$($n$,$ k$),$ where n and k are formal parameters. These numbers are called the binomial coefficients, and appear in a number of areas.

For example, they count the number of arrangements in a row that one can make from n objects, k of which are red, and n$-$k of which are green.

They also are the coefficients of xnyn$-$k in the expansion of $($x$+$y$)$n$.$ For instance, $($x $+$ y$)3$ may be written x$3+3$x$2$y $+3$xy$2+$ y$3,$ and $1,3,3,1$ are C$(3,0),$ C$(3,1),$ C$(3,2),$ and C$(3,3).$ If we write the binomial coefficients in a table, with k increasing from left to right, and n increasing as we go down the table, we produce what is known as Pascal$$s Triangle.

Below are the first four rows. Notice that it mirrors the definition, since each term is the XC$05$ sum of the one above it and the one above and to the left. $1111211331$ Write a complete Python program that prints the first n rows of Pascal's Triangle, where n is input by the user from the keyboard. Use your recursive function for computing C$($n$,$ k$)$ in writing the program."