Genocchi number

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

$\frac{2t}{e^t%2B1}=\sum_{n=1}^{\infty} G_n\frac{t^n}{n!}.$

The first few Genocchi numbers are 1, −1, 0, 1, 0, −3, 0, 17 (sequence A001469 in OEIS). G_n is 0 for odd n > 1.

It has been proven that −3 and 17 are the only prime Genocchi numbers.

They are related to Bernoulli numbers B_n by the formula

$G_n=2 \,(1-2^n) \,B_n.$

References