e = [1 + 1/fromIntegral t * sum (f . (n-) <$> [1..t]) | n <- [1..]] where f i = if i < 1 then 0 else e !! (i-1)
Standard input is empty
(1,1 % 1) (2,7 % 6) (3,49 % 36) (4,343 % 216) (5,2401 % 1296) (6,16807 % 7776) (7,117649 % 46656) (8,776887 % 279936) (9,5111617 % 1679616) (10,33495175 % 10077696) (11,218463217 % 60466176) (12,1417221463 % 362797056) (13,9136402849 % 2176782336) (14,58465788199 % 13060694016) (15,373014077521 % 78364164096) (16,2372610939895 % 470184984576) (17,15045525694465 % 2821109907456) (18,95126060008903 % 16926659444736) (19,599760535484593 % 101559956668416) (20,3772055737069207 % 609359740010496)