A141319 INVERTi transform of A141318.

2, 3, 8, 46, 252, 1558, 9800, 64115, 428546, 2921527, 20220128, 141746372, 1004278856, 7180301580, 51739691584, 375370204876, 2739615168344, 20100885190508, 148179065429664, 1096966770610372, 8151826588836472, 60787793832205004, 454719634089674432

Offset

1,1

Comments

Number of generators of degree n of the primitive Lie algebra of the Hopf algebra of 2-colored planar binary trees.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..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.

Maple

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

Mathematica

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

Crossrefs

Cf. A025225, A141318.

Sequence in context: A013208 A094370 A066084 * A369602 A001289 A103045

Adjacent sequences: A141316 A141317 A141318 * A141320 A141321 A141322

Keyword

nonn

Author

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

Status

approved