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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Nov 25 2018 *)

CROSSREFS

Cf. A003480.

Sequence in context: A296292 A287966 A148191 * A148192 A192531 A323864

Adjacent sequences:  A141309 A141310 A141311 * A141313 A141314 A141315

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

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Last modified January 24 19:03 EST 2022. Contains 350565 sequences. (Running on oeis4.)