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
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];
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]];
CROSSREFS
KEYWORD
nonn
AUTHOR
Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008
STATUS
approved