A141318 Euler transform of A025225.

1, 2, 7, 28, 139, 762, 4549, 28464, 184742, 1230348, 8362298, 57756888, 404218046, 2860222020, 20428192842, 147072637472, 1066221149519, 7776835940430, 57028407361537, 420199462347876, 3109418928328473, 23098206138595710, 172184651286785655, 1287629984135461888

Offset

0,2

Comments

Dimensions of the graded components of the domain of cocommutativity of the Hopf algebra of 2-colored planar binary trees.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

J.-C. Novelli and J.-Y. Thibon, Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions, arXiv:0806.3682 [math.CO], 2008.

Formula

a(n) ~ c * 8^n / n^(3/2), where c = 0.23667440081254669364903300472... . - Vaclav Kotesovec, Sep 04 2014

Maple

with(numtheory):
a:= proc(n) option remember;
      `if`(n=0, 1, add(add((2^d)*binomial(2*d-2, d-1),
                   d=divisors(j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jan 27 2012

Mathematica

a[n_] := a[n] = If[n==0, 1, Sum[Sum[2^d*Binomial[2*d-2, d-1], {d, Divisors[ j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 24 2016, after Alois P. Heinz *)

Crossrefs

Cf. A025225.

Sequence in context: A116539 A266467 A370509 * A276080 A352659 A030875

Adjacent sequences: A141315 A141316 A141317 * A141319 A141320 A141321

Keyword

nonn

Author

Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008

Extensions

a(0)=1 prepended by Alois P. Heinz, Jul 28 2017

Status

approved