Pentatope Number

A figurate number which is given by

where  is the th tetrahedral number. The first few pentatope numbers are 1, 5, 15, 35, 70, 126, ... (OEIS A000332). The generating function for the pentatope numbers is

REFERENCES:

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 55-57, 1996.

Sloane, N. J. A. Sequence A000332/M3853 in "The On-Line Encyclopedia of Integer Sequences."a