Example
Binomial transforms can be seen in difference tables. Consider the following:
| 0 | 1 | 10 | 63 | 324 | 1485 | |||||
| 1 | 9 | 53 | 261 | 1161 | ||||||
| 8 | 44 | 208 | 900 | |||||||
| 36 | 164 | 692 | ||||||||
| 128 | 528 | |||||||||
| 400 |
The top line 0, 1, 10, 63, 324, 1485,... (a sequence defined by (2n2 + n)3n − 2) is the binomial transform of the diagonal 0, 1, 8, 36, 128, 400,... (a sequence defined by n22n − 1).
Read more about this topic: Binomial Transform
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