0,3

Number of binary trees of height less than n.

The rightmost digits cycle (0,1,2,5,6,7,0,1,2,5,6,7,...). a(n) is prime for n = 2, 3, 5, ... a(n) is semiprime for n = 4, ... - Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 21 2005

Apart from the initial term a subsequence of A008318. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 17 2008

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 443-448.

R. K. Guy, How to factor a number, Proc. 5th Manitoba Conf. Numerical Math., Congress. Num. 16 (1975), 49-89.

R. Penrose, The Emperor's New Mind, Oxford, 1989, p. 122

M. Tainiter, Algebraic approach to stopping variable problems: Representation theory and applications. J. Combinatorial Theory 9 1970 148-161.

A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.

P. Flajolet and A. M. Odlyzko, Limit distributions of coefficients of iterates of polynomials with applications to combinatorial enumerations, Math. Proc. Camb. Phil. Soc., 96 (1984), 237-253.

C. Lenormand, Arbres et permutations II, see p. 6

Index entries for sequences of form a(n+1)=a(n)^2 + ...

a_n=B_{n-1}(1) where B_n(x)=1+xB_{n-1}(x)^2 is the generating function of trees of height <= n.

a(n) is asymptotic to c^(2^n) where c=1.2259024435287485386279474959130085213... - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 27 2002

c = b^(1/4) where b is the constant in Bottomley's formula in A004019. a(n) appears very asymptotic to c^(2^n) - Sum(k=1,infinity, A088674[k]/(2*c^(2^n))^(2*k-1)). - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Nov 17 2007

Cf. A038044.

Cf. A001699, A056207, A004019.

A143848, A143849. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 03 2008]

Adjacent sequences: A003092 A003093 A003094 this_sequence A003096 A003097 A003098

Sequence in context: A128595 A111195 A064006 this_sequence A023362 A138613 A090744

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), R. P. Stanley

Additional comments from Cyril Banderier (Cyril.Banderier(AT)inria.fr), Jun 05 2000