  In this note we prove a new explicit formula for the invariants of moduli
spaces of twisted Higgs bundles over P^1 and we relate these invariants to the
invariants of moduli spaces of representations of some infinite symmetric
quiver. The formula can be easily implemented for computations and it is in
agreement with the existing conjectures for the invariants of twisted Higgs
bundles over curves. Results of this note were presented in Oberwolfach in May
2014.
