Genocchi numbers

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The Genocchi numbers $G_n$ are given by the generating function $$\dfrac{2t}{e^t+1} = \displaystyle\sum_{k=0}^{\infty} G_n \dfrac{t^n}{n!}.$$

Properties[edit]

Proposition: The following formula holds: $$G_{2n}=2(1-2^{2n})B_{2n}= 2nE_{2n-1}(0),$$ where $G_{2n}$ denotes Genocchi numbers, $B_{2n}$ denotes Bernoulli numbers, and $E_{2n-1}$ denotes an Euler polynomial.

Proof: