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 A141314 Euler transform of A141313. 1
 1, 2, 11, 108, 1713, 36470, 969919, 30847464, 1142093211, 48275435126, 2295244558713, 121298268430124, 7056341421006321, 448203413035086358, 30870845475874376523, 2292084206324841742216, 182512808842356490744432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Dimensions of the graded components of the domain of cocommutativity 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 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: A207155 A292566 A053988 * A099933 A098437 A145163 Adjacent sequences: A141311 A141312 A141313 * A141315 A141316 A141317 KEYWORD nonn AUTHOR Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008 STATUS approved

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Last modified February 8 09:09 EST 2023. Contains 360138 sequences. (Running on oeis4.)