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A001927 Number of connected partially ordered sets with n labeled points.
(Formerly M2043 N0809)
12
1, 1, 2, 12, 146, 3060, 101642, 5106612, 377403266, 40299722580, 6138497261882, 1320327172853172, 397571105288091506, 166330355795371103700, 96036130723851671469482, 76070282980382554147600692, 82226869197428315925408327266 (list; graph; refs; listen; history; text; internal format)
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.

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

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..16.

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

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

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

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]

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

M. Erné and K. 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. A(x)=log(B(x)) where B(x) is e.g.f. of A001035.

MATHEMATICA

(* This is just a verification, given A001035 = {1, 1, 3, 19, 219, ...} *) max = 18; B[x_] := Sum[A001035[[k+1]]*x^k/k!, {k, 0, max}]; A[x_] := Sum[c[k]*x^k/k!, {k, 0, max}]; a[0] = 1; a[n_] := c[n] /. Solve[SeriesCoefficient[A[x] - Log[B[x]], {x, 0, n}] == 0] // First; Table[a[n], {n, 0, max}] (* Jean-François Alcover, Apr 17 2014 *)

CROSSREFS

Cf. A000112, A001035, A000608, A066303.

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

Sequence in context: A296137 A086928 A228551 * A289987 A105558 A279011

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

STATUS

approved

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Last modified February 18 17:08 EST 2018. Contains 299325 sequences. (Running on oeis4.)