Fibonacci factoriangular numbers

Let (Fm)m≥0 be the Fibonacci sequence given by F0=0, F1=1 and Fm+2=Fm+1+Fm, for all m≥0. In Castillo (2015), it is conjectured that 2,5 and 34 are the only Fibonacci numbers of the form n!+n(n+1)2, for some positive integer n. In this paper, we confirm the above conjecture.