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%I #12 Oct 09 2019 02:56:48
%S 1,2,4,12,31,92,256,772,2291,7000,21476,66804,208935,658924,2088628,
%T 6656820,21306270,68468796,220776444,714117012,2316229821,7531561676,
%U 24545492916,80160031076,262279882239,859660694960,2822177751148,9278647613760,30547880467863
%N Inverse Euler transform of A003480.
%C Dimensions of the graded components of the primitive Lie algebra of the Hopf algebra of noncommutative multisymmetric functions of level 2.
%H Alois P. Heinz, <a href="/A141312/b141312.txt">Table of n, a(n) for n = 0..1000</a>
%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.
%F a(n) ~ (2 + sqrt(2))^n / n. - _Vaclav Kotesovec_, Oct 09 2019
%p EULERi(INVERT([seq(n+1,n=1..20)]));
%t terms = 29;
%t mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];
%t 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]];
%t Join[{1}, EULERi[LinearRecurrence[{4, -2}, {2, 7}, terms-1]]] (* _Jean-François Alcover_, Nov 25 2018 *)
%Y Cf. A003480.
%K nonn
%O 0,2
%A Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Jun 26 2008
%E More terms from _Alois P. Heinz_, Feb 20 2017
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