The most surprising thing about this formula is its use of the Bernoulli numbers, and it is natural to ask why they appear. The answer is that it is not the B ’s which insist on entry, but the numbers A r = B r / r !. We use the notation where all other B with odd subscripts vanish, and those with even subscripts are alternately positive and negative. We shall often ignore the fact that A 3 , A 5 , .. vanish, thereby refusing to complicate formulae unnecessarily.