I'm unsure where this should go, but because it is related to a formula for , I've put it in here. The question is regarding this recursive formula for Bernoulli numbers

Essentially, we therefore have the following;

Given we also have

Then we can pair each for , to obtain

Where each . I then wanted to consider even and odd, but I'm unsure if this is even the right way to go about. If so, how on earth do you validate that recursive formula?

Thanks a lot in advance,

HTale.