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Search: id:A003430
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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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+0
3
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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; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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
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S. R. Finch, Series-parallel networks
Index entries for sequences related to posets
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 72
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FORMULA
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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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CROSSREFS
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Cf. A003431, A053554 (labeled N-free posets).
Sequence in context: A035350 A006570 A149928 this_sequence A149929 A149930 A149931
Adjacent sequences: A003427 A003428 A003429 this_sequence A003431 A003432 A003433
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. P. Stanley and Mira Bernstein (mira(AT)math.berkeley.edu)
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