A185161 G.f. = 1/(1-g(x)) where g(x) is the g.f. for A141309.

1, 2, 7, 36, 283, 2898, 36169, 524976, 8659186, 159736316, 3257811334, 72797444280, 1769125982092, 46466434382032, 1311960028913384, 39633438764146568, 1275742281105759813, 43593785716301112538, 1576217593145774955007

Offset: 0

Author

N. J. A. Sloane, Jan 23 2012

Keywords

• nonn
• changed

Links

• Jean-Christophe Novelli and Jean-Yves Thibon, Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions (2008); arXiv:0806.3682 [math.CO], 2008; Discrete Math. 310 (2010), no. 24, 3584-3606. See Eq. 37.

Crossrefs

Cf. A141309.

Essentially the same as A141308.

Programs

Mathematica

terms = 19;
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}] + O[x]^terms - 1)/x;
g[x_] = ((-1/(1 + x s) + O[x]^terms) + 1);
CoefficientList[1/(1 - g[x]) + O[x]^terms, x] (* Jean-François Alcover, Feb 13 2019 *)