  We study a certain linear automorphism of a vertex operator algebra induced
by the formal change of variable $f(x)=e^x-1$ and describe examples showing how
this relates the theory of vertex operator algebras to Bernoulli numbers,
Bernoulli polynomial values, and related numbers. We give a recursion for such
numbers derived using vertex operator relations, and study the Jacobi identity
for modified vertex operators that was introduced in work of Lepowsky.
