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Gaussian Brackets

Given quantities , , …, , the Gaussian bracket is defined as the sum of all following terms:
- the product ,
- all products that omit any pair of terms with consecutive indices,
- all products that omit any two pairs of terms, each with consecutive indices,
- all products that omit any three pairs of terms, each with consecutive indices,
- and so forth, where the empty product has the value 1 if is even.

This term was actually introduced by Euler, who used the notation . Euler or Gauss brackets have applications in number theory, combinatorics, etc.
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