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Pentatope Number

A figurate number which is given by

Ptop_n=1/4Te_n(n+3)=1/(24)n(n+1)(n+2)(n+3),

where Te_n is the nth tetrahedral number. The first few pentatope numbers are 1, 5, 15, 35, 70, 126, ... (OEIS A000332). The generating function for the pentatope numbers is

x/((1-x)^5)=x+5x^2+15x^3+35x^4+....

See also

Figurate Number, Tetrahedral Number

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References

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 55-57, 1996.Sloane, N. J. A. Sequence A000332/M3853 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Pentatope Number

Cite this as:

Weisstein, Eric W. "Pentatope Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PentatopeNumber.html

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