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A Pentatope Number is a figurate number (a number that can be represented by a regular geometric arrangement of equally spaced points) given by
where T_{n} is the nth tetrahedral number.
The first few pentatope numbers are 1, 5, 15, 35, 70, 126, ... and they are found in the fifth diagonal of Pascal's triangle:







1 








Row 0  






1 

1 







Row 1  





1 

2 

1 






Row 2  




1 
3 
3 

1 





Row 3  



1 

4 

6 

4 

1 




Row 4  


1 

5 

10 

10 

5 

1 



Row 5  

1 

6 

15 

20 

15 

6 

1 


Row 6  
1 

7 

21 

35 

35 

21 

7 

1 

Row 7  
1 

8 

28 

56 

70 

56 

28 

8 

1 
Row 8 
References
 Eric's Treasure Trove of Mathematics: Pentatope Number
 Eric's Treasure Trove of Mathematics: Figurate Number
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