A pentagonal pyramidal number is a figurate number obtained by adding the first 
pentagonal numbers, arranged
in layers as a pentagonal pyramid, where 
is a positive integer. The first few are 1, 6,
18, 40, 75, ... (OEIS A002411). The generating
function for the pentagonal pyramidal numbers is
 |
for 
.
The odd pentagonal pyramidal numbers are given by 1,
75, 405, 1183, 2601, ... (OEIS A015223), having
squares 1, 5625, 164025, ... (OEIS A014799),
while the even pentagonal pyramidal numbers are given
by 6, 18, 40, 126, 196, 288, ... (OEIS A015224),
having squares 36, 324, 1600, 15876, ... (OEIS A014800).
