Figurate Number Triangle
المؤلف:
Smith, D. E
المصدر:
A Source Book in Mathematics. New York: Dover
الجزء والصفحة:
p. 86
12-12-2020
969
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 
),
![[1 0 0 0 0 0 0 ...; 1 1 0 0 0 0 0 ...; 1 2 1 0 0 0 0 ...; 1 3 3 1 0 0 0 ...; 1 4 6 4 1 0 0 ...; 1 5 10 10 5 1 0 ...; 1 6 15 20 15 6 1 ...; 1 7 21 35 35 21 7 ...; | | | | | | | ...]](https://mathworld.wolfram.com/images/equations/FigurateNumberTriangle/NumberedEquation2.gif) |
(2)
|
Then we have the sum identities
REFERENCES:
Smith, D. E. A Source Book in Mathematics. New York: Dover, p. 86, 1984.
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