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A232974 Number of irreducible packed words of length n. 0

%I

%S 1,2,2,10,66,538,5170,56906,704226,9671930,145992338,2403271594,

%T 42869336130,824103252058,16991417367538,374154425946890,

%U 8765990409737634,217771226025864122,5718895163944768850,158315176568802482794,4608155971186431515394

%N Number of irreducible packed words of length n.

%C a(7) had a typo in the arXiv link on page 10 in Table 3 of i_n.

%H G. H. E. Duchamp, N. Hoang-Nghia, A. Tanasa, <a href="http://www.emis.de/journals/SLC/wpapers/s69vortrag/nguyen.pdf">A word Hopf algebra based on the selection/quotient principle</a>, Séminaire Lotharingien de Combinatoire 68 (2013), Article B68c.

%H G. H. E. Duchamp, N. Hoang-Nghia, A. Tanasa, <a href="http://arxiv.org/abs/1207.6522">A word Hopf algebra based on the selection/quotient principle</a>, arXiv:1207.6522 [math.CO], 2012-2013.

%F G.f.: 2 - (1 - 2*x / (1 - 1*x / (1 - 4*x / (1 - 2*x / (1 - 6*x ...))))) = 2 - 1 / f(x) where f() is the g.f. for A000629. - _Michael Somos_, Mar 05 2014

%F INVERT transform of a(1..) = [2, 2, 10, 66, 538, 5170, 56906, ...] is A000629(1..) = [2, 6, 26, 150, 1082, 9366, 94586, ...]. - _Michael Somos_, Mar 06 2014

%e G.f. = 1 + 2*x + 2*x^2 + 10*x^3 + 66*x^4 + 538*x^5 + 5170*x^6 + 56906*x^7 + ...

%e The packed irreducible words for n=1 are 0, 1; for n=2 are 11, 21; for n=3 are 101, 111, 121, 201, 211, 212, 221, 231, 312, 321. - _Michael Somos_, Mar 05 2014

%t nmax = 21;

%t A629[x_] = Sum[PolyLog[-n, 1/2] x^n, {n, 0, nmax}];

%t CoefficientList[2 - 1/A629[x] + O[x]^nmax, x] (* _Jean-François Alcover_, Aug 17 2018, after _Michael Somos_ *)

%Y Cf. A000629.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Dec 06 2013

%E a(11)-a(20) from _Michael Somos_, Mar 05 2014

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Last modified March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)