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A232974 Number of irreducible packed words of length n. 0
1, 2, 2, 10, 66, 538, 5170, 56906, 704226, 9671930, 145992338, 2403271594, 42869336130, 824103252058, 16991417367538, 374154425946890, 8765990409737634, 217771226025864122, 5718895163944768850, 158315176568802482794, 4608155971186431515394 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..20.

G. H. E. Duchamp, N. Hoang-Nghia, A. Tanasa, A word Hopf algebra based on the selection/quotient principle, Séminaire Lotharingien de Combinatoire 68 (2013), Article B68c.

G. H. E. Duchamp, N. Hoang-Nghia, A. Tanasa, A word Hopf algebra based on the selection/quotient principle, arXiv:1207.6522 [math.CO], 2012-2013.

FORMULA

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

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

EXAMPLE

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

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

MATHEMATICA

nmax = 21;

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

CoefficientList[2 - 1/A629[x] + O[x]^nmax, x] (* Jean-François Alcover, Aug 17 2018, after Michael Somos *)

CROSSREFS

Cf. A000629.

Sequence in context: A059494 A052647 A326983 * A181334 A032034 A002250

Adjacent sequences:  A232971 A232972 A232973 * A232975 A232976 A232977

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 06 2013

EXTENSIONS

a(11)-a(20) from Michael Somos, Mar 05 2014

STATUS

approved

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Last modified December 3 11:58 EST 2020. Contains 338900 sequences. (Running on oeis4.)