A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1 either from left to right or from right to left. The first few numbers of this kind are : 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001, 1365 (sequence A000332 in OEIS) Image:Pentatope of 70 spheres animation.gif Pentatope numbers belong in the class of figurate numbers, which can be represented as regular, discrete geometric patterns. The formula for the nth pentatopic number is: Pentatopal numbers can also be represented as the sum of the first n tetrahedral numbers.