A141315 INVERTi transform of A141314.

2, 7, 72, 1276, 28944, 805288, 26462232, 1003888638, 43223532564, 2084457594706, 111392693178728, 6538003816585018, 418294118782252428, 28983591342405843026, 2162792477786790459080, 172955289365222965693543

Offset

1,1

Comments

Number of generators of degree n of the primitive Lie algebra of the Hopf algebra of 2-colored parking functions.

Links

Table of n, a(n) for n=1..16.

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

INVERTi([seq(d(n), n=1..20)]); # where d(n) is A141314.

Mathematica

terms = 16;
s = (1 - 1/(1 + Sum[(n + 1)^(n - 1)*t^n, {n, 1, terms}]))/t + O[t]^(terms);
A141313 = 2^Range[terms]*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];
A141314 = Join[{1}, EulerTransform[A141313]];
INVERTi[a_] := Module[{t1, x, b, n}, n=Length[a]; b = Sum[a[[i+1]] x^i, {i, 0, n-1}]; t1 = Series[-1/(1+x*b), {x, 0, n}]; CoefficientList[1+t1, x]];
A141315 = INVERTi[A141314 // Rest] // Rest (* Jean-François Alcover, Feb 17 2019 *)

Crossrefs

Cf. A141313, A141314.

Sequence in context: A100360 A061421 A304192 * A215637 A119811 A319621

Adjacent sequences: A141312 A141313 A141314 * A141316 A141317 A141318

Keyword

nonn

Author

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

Status

approved