

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
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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. HoangNghia, 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. HoangNghia, A. Tanasa, A word Hopf algebra based on the selection/quotient principle, arXiv:1207.6522 [math.CO], 20122013.


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] (* JeanFrançois 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



