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Date: 8-11-2020
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Date: 22-12-2019
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Date: 5-2-2020
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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) |
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(4) |
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(5) |
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(6) |
REFERENCES:
Smith, D. E. A Source Book in Mathematics. New York: Dover, p. 86, 1984.
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