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

Linear automorphisms of vertex operator algebras associated with formal changes of variable and Bernoulli-type numbers