For prime n, it is also the number of generalized knockout tournament seedings with n players in one match and n rounds (see formula below).  Alexander Karpov, Dec 14 2017
Next term is too large to include.
From Robert G. Wilson v, Dec 14 2017: (Start)
a(4) = 4125147631... (370 digits)...3291015625,
a(5) = 3483655217... (7923 digits)...3819109376,
a(6) = 2196422024... (164237 digits)...0161431552,
a(7) = 4948281440... (4005981 digits)...0000000000,
a(8) = 4242413765...(102886160 digits)...4619140625,
(End)
