A006059 Number of connected labeled T_0-T_4-topologies with n points. (Formerly M1948)

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

Offset

0,3

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)

Formula

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

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 *)

Crossrefs

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

Sequence in context: A132621 A108992 A058164 * A277406 A182947 A006041

Adjacent sequences: A006056 A006057 A006058 * A006060 A006061 A006062

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

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

Status

approved