Let V p (λ) be the collection of all functions f defined in the unit disc D having a simple pole at z= p where 0 < p< 1 and analytic in D {p} with f(0) = 0 = f ′ (0) – 1 and satisfying the differential inequality | (z/ f(z)) 2 f ′ (z) – 1 | < λ for z∈ D, 0 < λ≤ 1. Each f∈ V p (λ) has the following Taylor expansion: f(z)=z+∑n=2∞an(f)zn,|z|<p.We recently conjectured that |an(f)|≤1-(λp2)npn-1(1-λp2)forn≥3,while investigating functions in the class V p (λ). In the present article, we first obtain a representation formula for functions in this class. Using this, we prove the aforementioned conjecture for n= 3 , 4 , 5 whenever p belongs to certain subintervals of (0, 1). Also we determine non sharp bounds for |an(f)|,n≥3 and for |an+1(f)-an(f)/p|,n≥2.