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

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

Then we have the sum identities

**References**

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

© 1996-9

1999-05-26