A141314 Euler transform of A141313.

1, 2, 11, 108, 1713, 36470, 969919, 30847464, 1142093211, 48275435126, 2295244558713, 121298268430124, 7056341421006321, 448203413035086358, 30870845475874376523, 2292084206324841742216, 182512808842356490744432

Offset

1,2

Comments

Dimensions of the graded components of the domain of cocommutativity of the Hopf algebra of 2-colored parking functions.

Links

Table of n, a(n) for n=1..17.

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

EULER([seq(c(n, n=1..20)]); # where c(n) is A141313.

Mathematica

terms = 17;
s = (1 - 1/(1 + Sum[(n+1)^(n-1)*t^n, {n, 1, terms}]))/t + O[t]^(terms-1);
A141313 = 2^Range[terms-1]*CoefficientList[s, t];
did[m_, n_] := If[Mod[m, n] == 0, 1, 0];
EulerTransform[seq_] := Module[{coeff, final = {}}, coeff = Table[Sum[d* did[i, d]*seq[[d]], {d, 1, i}], {i, 1, Length[seq]}]; For[i = 1, i <= Length[seq], i++, AppendTo[final, (coeff[[i]] + Sum[coeff[[d]]*final[[i - d]], {d, 1, i-1}])/i]]; final];
Join[{1}, EulerTransform[A141313]] (* Jean-François Alcover, Feb 17 2019 *)

Crossrefs

Cf. A141313.

Sequence in context: A292566 A365106 A053988 * A363481 A099933 A098437

Adjacent sequences: A141311 A141312 A141313 * A141315 A141316 A141317

Keyword

nonn

Author

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

Status

approved