A086367 (1/p)*(F(p^2+1)-1) where p runs through the primes (except p=5) and F(k) is the k-th Fibonacci number.

2, 18, 1798038432, 1275306059408992299902160, 11600333847446766979664251842465168, 106287391548458779396407861152154912538870151693018243514432