  Consider zero-dimensional Donaldson-Thomas invariants of a toric threefold or
toric Calabi-Yau fourfold. In the second case, invariants can be defined using
a tautological insertion. In both cases, the generating series can be expressed
in terms of the MacMahon function. In the first case, this follows from a
theorem of Maulik-Nekrasov-Okounkov-Pandharipande. In the second case, this
follows from a conjecture of the authors and a (more general $K$-theoretic)
conjecture of Nekrasov.
  In this paper, we consider formal analogues of these invariants in any
dimension $d \not \equiv 2 \ \mathrm{mod} \, 4$. The direct analogues of the
above-mentioned conjectures fail in general when $d>4$, showing that dimensions
3 and 4 are special. Surprisingly, after appropriate specialization of the
equivariant parameters, the conjectures seem to hold in all dimensions.
