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A001927
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Number of connected partially ordered sets with n labeled points.
(Formerly M2043 N0809)
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16
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1, 1, 2, 12, 146, 3060, 101642, 5106612, 377403266, 40299722580, 6138497261882, 1320327172853172, 397571105288091506, 166330355795371103700, 96036130723851671469482, 76070282980382554147600692, 82226869197428315925408327266, 120722306604121583767045993825620, 239727397782668638856762574296226842
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OFFSET
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0,3
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REFERENCES
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K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184. [Annotated scan of pages 180 and 183 only]
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FORMULA
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E.g.f. A(x)=log(B(x)) where B(x) is e.g.f. of A001035.
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MATHEMATICA
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A001035 = {1, 1, 3, 19, 219, 4231, 130023, 6129859, 431723379, 44511042511, 6611065248783, 1396281677105899, 414864951055853499, 171850728381587059351, 98484324257128207032183, 77567171020440688353049939, 83480529785490157813844256579, 122152541250295322862941281269151, 241939392597201176602897820148085023};
B[x_] = Sum[A001035[[k+1]]*x^k/k!, {k, 0, max}];
A[x_] = 1 + Log[B[x]];
CoefficientList[A[x] + O[x]^(max-1), x]*Range[0, max-2]! (* Jean-François Alcover, Apr 17 2014, updated Aug 30 2018 *)
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CROSSREFS
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KEYWORD
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nonn,nice,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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