A141312 Inverse Euler transform of A003480.

1, 2, 4, 12, 31, 92, 256, 772, 2291, 7000, 21476, 66804, 208935, 658924, 2088628, 6656820, 21306270, 68468796, 220776444, 714117012, 2316229821, 7531561676, 24545492916, 80160031076, 262279882239, 859660694960, 2822177751148, 9278647613760, 30547880467863

Offset: 0

Author

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

Keywords

• nonn

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.

Crossrefs

Cf. A003480.

Programs

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 *)

Formula

a(n) ~ (2 + sqrt(2))^n / n. - Vaclav Kotesovec, Oct 09 2019

Extensions

More terms from Alois P. Heinz, Feb 20 2017