Confluent hypergeometric expansions of the confluent Heun function governed by two-term recurrence relations

We show that there exist infinitely many nontrivial choices of parameters of the single confluent Heun equation for which the three-term recurrence relations governing the expansions of the solutions in terms of the confluent hypergeometric functions ₁ F ₁ and ₀ F ₁ are reduced to two-term ones. In such cases the expansion coefficients are explicitly calculated in terms of the Euler gamma functions.