A pentatope number is the four-dimensional analogue of the [[triangular]] and [[tetrahedral]] numbers — it counts the points in a regular 4-simplex (a "pentatope"). The sequence: 1, 5, 15, 35, 70, 126, 210, 330, 495, 715. Each is a binomial coefficient, \(\binom{k+3}{4}\), so the pentatope numbers form the fifth diagonal of Pascal's triangle (after the 1s, the counting numbers, the triangular numbers, and the tetrahedral numbers).
The central pentatope number 70 is famous for a different reason: it's the only number whose square (4900) is also a square pyramidal number — the cannonball problem's solution.