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A003430 Number of unlabeled N-free posets (i.e., generated by unions and sums) with n nodes.
(Formerly M1476)
8
1, 2, 5, 15, 48, 167, 602, 2256, 8660, 33958, 135292, 546422, 2231462, 9199869, 38237213, 160047496, 674034147, 2854137769, 12144094756, 51895919734, 222634125803, 958474338539, 4139623680861, 17931324678301, 77880642231286 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.39 (which deals with the labeled case of the same sequence).

LINKS

Table of n, a(n) for n=1..25.

P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102; also in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89-102.

Frédéric Fauvet, L. Foissy, D. Manchon, Operads of finite posets, arXiv preprint arXiv:1604.08149 [math.CO], 2016.

S. R. Finch, Series-parallel networks

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 72

R. P. Stanley, Enumeration of posets generated by disjoint unions and ordinal sums, Proc. Amer. Math. Soc. 45 (1974), 295-299. Math. Rev. 50 #4416.

R. P. Stanley, Letter to N. J. A. Sloane, c. 1991

Index entries for sequences related to posets

FORMULA

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + ... satisfies A(x) = exp( Sum_{k=1..inf} (1/k)*(A(x^k) + 1/A(x^k) - 2 + x^k) ).

MATHEMATICA

terms = 25; A[_] = 1; Do[A[x_] = Exp[Sum[(1/k)*(A[x^k] + 1/A[x^k] - 2 + x^k), {k, 1, terms + 1}]] + O[x]^(terms + 1) // Normal, terms + 1];

CoefficientList[A[x], x] // Rest (* Jean-François Alcover, Jun 29 2011, updated Jan 12 2018 *)

CROSSREFS

Cf. A003431, A053554 (labeled N-free posets).

Sequence in context: A035350 A006570 A149928 * A149929 A149930 A189924

Adjacent sequences:  A003427 A003428 A003429 * A003431 A003432 A003433

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane and Richard Stanley and Mira Bernstein

STATUS

approved

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Last modified October 15 21:06 EDT 2018. Contains 316237 sequences. (Running on oeis4.)