A145549 Number of distinct values taken by 9^9^...^9 (with n 9's and parentheses inserted in all possible ways).

1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4766, 12485, 32969, 87795, 235326, 634664, 1720573, 4686829, 12820504, 35204254, 97001655, 268120807, 743236814, 2065709551, 5755253457

Offset: 1

Author

Jon E. Schoenfield, Oct 13 2008

Keywords

• more
• nonn

Comments

The subsequence of primes begins 2, 719, 32969. No more through a(26). [Jonathan Vos Post, Apr 02 2011]

Links

• R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis, Amer. Math. Monthly 80 (8) (1973), 868-876.
• Jonathan Vos Post, The Four Nines problem.
• Index entries for sequences related to parenthesizing

Crossrefs

Cf. A002845, A003018, A003019, A145545, A145546, A145547, A145548, A145550, A000081.