  We prove asymptotics and study sign patterns for coefficients in expansions
of elements in the Habiro ring which satisfy a strange identity. As an
application, we prove asymptotics and discuss positivity for the generalized
Fishburn numbers which arise from the Kontsevich-Zagier series associated to
the colored Jones polynomial for a family of torus knots. This extends Zagier's
result on asymptotics for the Fishburn numbers.
