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 (jvospost2(AT)yahoo.com), Jul 21 2005

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

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.

Adjacent sequences: A003092 A003093 A003094 this_sequence A003096 A003097 A003098

Sequence in context: A128595 A111195 A064006 this_sequence A023362 A090744 A041571

nonn,easy,nice

njas, R. P. Stanley

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