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A141312
Inverse Euler transform of A003480.
1
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
0,2
COMMENTS
Dimensions of the graded components of the primitive Lie algebra of the Hopf algebra of noncommutative multisymmetric functions of level 2.
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
Cf. A003480.
Sequence in context: A296292 A287966 A148191 * A148192 A373648 A192531
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