Who is asking: Student
It's called Pascal's Triangle. The first few rows are below. The first row is 1, and the second row is 1 1. Each successive row starts and ends with a 1 and for each other position the number is "the sum of the two numbers above it". For example in the 4th row the first 3 (the one I shaded) is the sum of the shaded 1 and 2 in the row above.
The numbers in the triangle are called the binomial coefficients. As you suggested they are the coefficients in the expansion of
(the coefficients are 1 3 3 1)