A centered pentachoric number is a figurate number that represents a pentachoron.
The first such numbers are: 1, 6, 21, 56, 126, 251, 456, 771, 1231, 1876, 2751, 3906, 5396, 7281, … (sequence A008498 in the OEIS).
Centered pentachoric numbers can also be represented as the sum of the first n pentatope numbers.
References
Centered pentachoric number Wikipedia(Text) CC BY-SA