Write a program that calculates triangle numbers by using a recursive function. A triangle number is the sum of all whole numbers from 1 to N, in which N is the number specified. For example, triangle (5) = 5 + 4 + 3 + 2 + 1. A triangular number or triangle number counts the objects that can form an triangle, as in the diagram on the right. The n th triangular number is the number of dots composing a triangle with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers (sequence A000217 in the OEIS), starting at the 0 th triangular number is 0 1 3 6 10 13 15 21 28 36 45 55 66 78 91 105 120 136 153 171 190 210 231 253 276 300 325 351 378 406 435 465 496 526 561 595 630 666 The triangle numbers are given by the following explicit formulas T_n = sigma^n_k = 1 + 2 + 3 + middot middot middot + n = n (n + 1)/2 = (n + 1 2), where (n + 1 2) is a binomial coefficient. It represents the number of distinct pairs that can be selected from n + 1 objects, and it is read aloud as "n plus one choose two