

A003430


Number of unlabeled seriesparallel 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
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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

JeanFrançois Alcover, Table of n, a(n) for n = 1..100
B. I. Bayoumi, M. H. ElZahar and S. M. Khamis, Asymptotic enumeration of Nfree partial orders, Order 6 (1989), 219232.
P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89102; also in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89102.
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, Seriesparallel networks
S. R. Finch, Seriesparallel 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 Nfree posets, Discrete Math. 275 (2004), no. 13, 165175.
R. P. Stanley, Enumeration of posets generated by disjoint unions and ordinal sums, Proc. Amer. Math. Soc. 45 (1974), 295299. 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 (* JeanFrançois Alcover, Jun 29 2011, updated Jan 12 2018 *)


CROSSREFS

Cf. A003431, A053554 (labeled Nfree 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



