A141309 INVERTi transform of A141308.

2, 3, 16, 158, 1796, 24250, 372656, 6429927, 122956714, 2581840735, 59084565968, 1464445686726, 39101805324620, 1119446453417490, 34220008384633264, 1112764183812405300, 38362648544330997488, 1397884269388233025156

Offset: 1

Author

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

Keywords

• nonn

Comments

Number of generators of degree n of the (free) primitive Lie algebra of the Hopf algebra of free quasi-symmetric functions of level 2.

Links

• 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.

Crossrefs

Cf. A003319, A141307, A141308.

Programs

Maple

INVERTi([seq(d(n,n=1..20)]); # where d(n) is A141308

Mathematica

terms = 18;
c[0] = 0; c[n_] := c[n] = n! - Sum[k! c[n-k], {k, 1, n-1}];
s = (Product[1/(1-x^k)^(2^k c[k]), {k, 1, terms+1}] + O[x]^(terms+1)-1)/x;
CoefficientList[-1/(1 + x s) + O[x]^(terms+1), x] // Rest (* Jean-François Alcover, Feb 13 2019 *)