Genocchi number

In mathematics, the Genocchi numbers G_n, named after Angelo Genocchi, are a sequence of integers that satisfy the relation

The first few Genocchi numbers are 1, −1, 0, 1, 0, −3, 0, 17 (sequence in the OEIS), see  .

There are two cases for ${\displaystyle G_{n}}$.

  is an autosequence (a sequence whose inverse binomial transform is the signed sequence) of the first kind (its main diagonal is 0's =  ). An autosequence of the second kind has its main diagonal equal to the first upper diagonal multiplied by 2. Example:   /  .

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