0,4

Also number of asymmetric rooted plane trees with n+1 nodes (Christian Bower).

Conjecturally, number of irreducible alternating Euler sums of depth n and weight 3n.

a(n+1) is inverse Euler transform of A000108. Inverse Witt transform of A006177.

Dimension of the degree n part of the primitive Lie algebra of the Hopf algebra CQSym (Catalan Quasi-Symmetric functions) - Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 22 2006

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 336 (4.4.64)

D. J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory

J.-C. Novelli and J.-Y. Thibon, Hopf algebras and dendriform structures arising from parking functions

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

Index entries for sequences related to rooted trees

Index entries for sequences related to Lyndon words

prod_n (1-x^n)^{a[ n ]} = 2/(1+\sqrt{1-4x}); a[ n ] = (1/2n) sum_{d|n} \mu(n/d) {2d \choose d}. Also Moebius transform of A003239 (Christian Bower).

(PARI) a(n)=if(n<1, n==0, sumdiv(n, d, moebius(n/d)*binomial(2*d, d))/2/n)

Cf. A003239, A005354, A000740. a(n)=A060165(n)/2.

Cf. A007727, A086655.

Sequence in context: A018789 A093969 A006177 this_sequence A088327 A007563 A050383

Adjacent sequences: A022550 A022551 A022552 this_sequence A022554 A022555 A022556

nonn

David Broadhurst (D.Broadhurst(AT)open.ac.uk)