∀ {R : Type u_1} [inst : CommSemiring R] [inst_1 : TopologicalSpace R] [T2Space R] (f : ℕ → ℕ → R),
  Nat.Partition.genFun f = ∏' (i : ℕ), (1 + ∑' (j : ℕ), f (i + 1) (j + 1) • PowerSeries.X ^ ((i + 1) * (j + 1)))