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Pentatope number
Figurate number; number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1 either from left to right or from right to left
In number theory, a pentatope number (or hypertetrahedral number or triangulo-triangular number) is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1, either from left to right or from right to left. It is named because it represents the number of 3-dimensional unit spheres which can be packed into a pentatope (a 4-dimensional tetrahedron) of increasing side lengths.
From Wikipedia
In number theory, a pentatope number (or hypertetrahedral number or triangulo-triangular number) is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1, either from left to right or from right to left. It is named because it represents the number of 3-dimensional unit spheres which can be packed into a pentatope (a 4-dimensional tetrahedron) of increasing side lengths. The first few numbers of this kind are: 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001, 1365 (sequence A000332 in the OEIS) Pentatope numbers belong to the class of figurate numbers, which can be represented as regular, discrete geometric patterns.
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