A006059 Number of connected labeled T_0-T_4-topologies with n points.

1, 1, 2, 9, 76, 1095, 25386, 910161, 49038872, 3885510411, 445110425110, 72721717736613, 16755380125270788, 5393244363726095487, 2405910197342218830914, 1477264863856923105482745, 1241074736327051013648799024, 1419169006353332682835352361843

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Herman Jamke, Table of n, a(n) for n = 0..19
• M. Erné, Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen, Manuscripta Math., 11 (1974), 221-259.
• M. Erné, Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen, Manuscripta Math., 11 (1974), 221-259. (Annotated scanned copy)

Crossrefs

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

Programs

Mathematica

A001035 = Cases[Import["https://oeis.org/A001035/b001035.txt", "Table"], {, }][[All, 2]];
a[n_] := If[n == 0, 1, n A001035[[n]]];
a /@ Range[0, Length[A001035]] (* Jean-François Alcover, Dec 30 2019 *)

Formula

a(n) = n*A001035(n-1) for n>=1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008

Extensions

More terms from Detlef Pauly (dettodet(AT)yahoo.de), Dec 27 2001