A141314 - OEIS

%I #7 Feb 17 2019 08:51:53

%S 1,2,11,108,1713,36470,969919,30847464,1142093211,48275435126,

%T 2295244558713,121298268430124,7056341421006321,448203413035086358,

%U 30870845475874376523,2292084206324841742216,182512808842356490744432

%N Euler transform of A141313.

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

%H J.-C. Novelli and J.-Y. Thibon, <a href="https://arxiv.org/abs/0806.3682">Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions</a>, arXiv:0806.3682 [math.CO], 2008.

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

%t terms = 17;

%t s = (1 - 1/(1 + Sum[(n+1)^(n-1)*t^n, {n, 1, terms}]))/t + O[t]^(terms-1);

%t A141313 = 2^Range[terms-1]*CoefficientList[s, t];

%t did[m_, n_] := If[Mod[m, n] == 0, 1, 0];

%t 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];

%t Join[{1}, EulerTransform[A141313]] (* _Jean-François Alcover_, Feb 17 2019 *)

%Y Cf. A141313.

%K nonn

%O 1,2

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