OFFSET
0,2
COMMENTS
Dimensions of the graded components of the primitive Lie algebra of the Hopf algebra of noncommutative multisymmetric functions of level 2.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
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.
FORMULA
a(n) ~ (2 + sqrt(2))^n / n. - Vaclav Kotesovec, Oct 09 2019
MAPLE
EULERi(INVERT([seq(n+1, n=1..20)]));
MATHEMATICA
terms = 29;
mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];
EULERi[b_] := Module[{a, c, i, d}, c = {}; For[i=1, i <= Length[b], i++, c = Append[c, i b[[i]] - Sum[c[[d]] b[[i-d]], {d, 1, i-1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i) Sum[mob[i, d] c[[d]], {d, 1, i}]]]; Return[a]];
Join[{1}, EULERi[LinearRecurrence[{4, -2}, {2, 7}, terms-1]]] (* Jean-François Alcover, Nov 25 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008
EXTENSIONS
More terms from Alois P. Heinz, Feb 20 2017
STATUS
approved