Figurate Number Triangle

A Pascal's triangle written in a square grid and padded with zeros, as written by Jakob Bernoulli (Smith 1984). The figurate number triangle therefore has entries

(1)

where  is the row number,  the column number, and  a binomial coefficient. Written out explicitly (beginning each row with ),

(2)

Then we have the sum identities

			(3)
			(4)
			(5)
			(6)

REFERENCES:

Smith, D. E. A Source Book in Mathematics. New York: Dover, p. 86, 1984.