A001927 Number of connected partially ordered sets with n labeled points. (Formerly M2043 N0809)

1, 1, 2, 12, 146, 3060, 101642, 5106612, 377403266, 40299722580, 6138497261882, 1320327172853172, 397571105288091506, 166330355795371103700, 96036130723851671469482, 76070282980382554147600692, 82226869197428315925408327266, 120722306604121583767045993825620, 239727397782668638856762574296226842

Offset

0,3

References

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).

Links

Table of n, a(n) for n=0..18.

C. M. Bender et al., Combinatorics and field theory, arXiv:quant-ph/0604164, 2006.

Gunnar Brinkmann and Brendan D. McKay, Posets on up to 16 Points, Order 19(2) (2002), 147-179. See Table II, up to 18 points.

Kim Ki-Hang Butler and George Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.

Kim Ki-Hang Butler and George 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]

Sangmin Chun, Gangyong Lee, Mauricio Medina-Barcenas, and Cosmin S. Roman, Rudimentary Structural Matrix Rings, J. Alg. Appl. (2026). See p. 12.

Marcel Erné, Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen, Manuscripta Math., 11 (1974), 221-259.

Marcel Erné, Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen, Manuscripta Math. 11 (1974), 221-259. (Annotated scanned copy)

Marcel Erné and Kurt Stege, Counting Finite Posets and Topologies, Order 8 (1991), 247-265.

N. J. A. Sloane, List of sequences related to partial orders, circa 1972

J. A. Wright, There are 718 6-point topologies, quasiorderings and transgraphs, Preprint, 1970 [Annotated scanned copy]

J. A. Wright, Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences.

Index entries for sequences related to posets

Formula

E.g.f.: log(B(x)) where B(x) is e.g.f. of A001035.

Mathematica

A001035 = {1, 1, 3, 19, 219, 4231, 130023, 6129859, 431723379, 44511042511, 6611065248783, 1396281677105899, 414864951055853499, 171850728381587059351, 98484324257128207032183, 77567171020440688353049939, 83480529785490157813844256579, 122152541250295322862941281269151, 241939392597201176602897820148085023};
max = Length[A001035]-1;
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 *)

Crossrefs

Cf. A000112, A001035, A000608, A066303, A342501 (refined by rank).

Sequences in the Erné (1974) paper: A000798, A001035, A006056, A006057, A001929, A001927, A006058, A006059, A000110.

Sequence in context: A296137 A086928 A228551 * A289987 A105558 A322399

Adjacent sequences: A001924 A001925 A001926 * A001928 A001929 A001930

Keyword

nonn,nice,hard

Author

N. J. A. Sloane

Extensions

More terms from Christian G. Bower, Dec 12 2001

a(17)-a(18) using data from A001035 from Alois P. Heinz, Aug 30 2018

Status

approved