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A003430 Number of unlabeled series-parallel posets (i.e., generated by unions and sums) with n nodes.
(Formerly M1476)
13
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

Jean-François Alcover, Table of n, a(n) for n = 1..100

B. I. Bayoumi, M. H. El-Zahar and S. M. Khamis, Asymptotic enumeration of N-free partial orders, Order 6 (1989), 219-232.

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.

Uli Fahrenberg, Christian Johansen, Georg Struth, Ratan Bahadur Thapa, Generating Posets Beyond N, arXiv:1910.06162 [cs.FL], 2019.

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

S. R. Finch, Series-parallel networks

S. R. Finch, Series-parallel networks, July 7, 2003. [Cached copy, with permission of the author]

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

Soheir M. Khamis, Height counting of unlabeled interval and N-free posets, Discrete Math. 275 (2004), no. 1-3, 165-175.

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} (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 A337262 A149930

Adjacent sequences:  A003427 A003428 A003429 * A003431 A003432 A003433

KEYWORD

easy,nonn,nice

AUTHOR

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

EXTENSIONS

Name corrected by Salah Uddin Mohammad, Jun 07 2020

STATUS

approved

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Last modified November 27 09:32 EST 2020. Contains 338679 sequences. (Running on oeis4.)