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A058350
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Number of labeled series-parallel posets on n nodes that are not a nontrivial ordinal sum.
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3
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1, 1, 7, 73, 1051, 19381, 436087, 11585953, 354981571, 12322179901, 477938035807, 20485584143113, 961567521142411, 49054912287659461, 2702571588828034567, 159911968233095867953, 10114120854154243738771, 680943323845807848142861
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Let ( T, < ) and ( U, < ) be posets with T and U disjoint. Their ordinal sum is ( T union U, < ) where x<y if x<y and both in T or both in U, or x in T and y in U. Note ordinal sum is not commutative.
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REFERENCES
| R. P. Stanley, Enumeration of posets generated by disjoint unions and ordinal sums. Proc. Amer. Math. Soc. 45 (1974), 295-299
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.39, page 133, h(n).
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LINKS
| Index entries for sequences related to posets
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MAPLE
| (continue from A053554) t1 := (EGF053554/(1+EGF053554); t2 := series(t1, x, 30); SERIESTOLISTMULT(t2);
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MATHEMATICA
| max = 18; S053554 = InverseSeries[ Series[ Log[1+x] - x^2/(1+x), {x, 0, max}], x]; Drop[ CoefficientList[ Series[ S053554 / (1+S053554), {x, 0, max}], x]* Range[0, max]!, 1] (* From Jean-François Alcover, Nov 29 2011, after Maple *)
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CROSSREFS
| A053554(n) = A058349(n) + A058350(n) (n>=2).
Sequence in context: A084363 A050352 A112939 * A048174 A134281 A051154
Adjacent sequences: A058347 A058348 A058349 * A058351 A058352 A058353
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 16 2000
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