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Pentatope Number

A Figurate Number which is given by

{\it Ptop}_n={\textstyle{1\over 4}}{\it Te}_n(n+3)={\textstyle{1\over 24}} n(n+1)(n+2)(n+3),

where ${\it Te}_n$ is the $n$th Tetrahedral Number. The first few pentatope numbers are 1, 5, 15, 35, 70, 126, ... (Sloane's A000332). The Generating Function for the pentatope numbers is


See also Figurate Number, Tetrahedral Number


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

© 1996-9 Eric W. Weisstein