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A003430
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Number of unlabeled N-free posets (i.e. generated by unions and sums) with n nodes.
(Formerly M1476)
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5
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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; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.39 (which deals with the labeled case of the same sequence).
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LINKS
| S. R. Finch, Series-parallel networks
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 72
Index entries for sequences related to posets
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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) ).
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MATHEMATICA
| m=25; c[0]=1; c[1]=1; gf[x_] = Sum[c[k]*x^k, {k, 0, m}];
se = Series[ Log[gf[x]] - Sum[(1/k)*(gf[x^k] + 1/gf[x^k] - 2 + x^k), {k, 1, m}], {x, 0, m}];
First[ Array[c, m] /. Solve[ Thread[ CoefficientList[se, x] == 0]]] (* From Jean-François Alcover, Jun 29 2011 *)
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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
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KEYWORD
| easy,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), R. P. Stanley and Mira Bernstein (mira(AT)math.berkeley.edu)
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