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A006059 Number of connected labeled T_0-T_4-topologies with n points.
(Formerly M1948)
9

%I M1948

%S 1,1,2,9,76,1095,25386,910161,49038872,3885510411,445110425110,

%T 72721717736613,16755380125270788,5393244363726095487,

%U 2405910197342218830914,1477264863856923105482745,1241074736327051013648799024,1419169006353332682835352361843

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

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

%H Herman Jamke, <a href="/A006059/b006059.txt">Table of n, a(n) for n = 0..19</a>

%H M. Erné, <a href="http://dx.doi.org/10.1007/BF01173716">Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen</a>, Manuscripta Math., 11 (1974), 221-259.

%H M. Erné, <a href="/A006056/a006056.pdf">Struktur- und Anzahlformeln für Topologien auf Endlichen Mengen</a>, Manuscripta Math., 11 (1974), 221-259. (Annotated scanned copy)

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

%t A001035 = Cases[Import["https://oeis.org/A001035/b001035.txt", "Table"], {_, _}][[All, 2]];

%t a[n_] := If[n == 0, 1, n A001035[[n]]];

%t a /@ Range[0, Length[A001035]] (* _Jean-François Alcover_, Dec 30 2019 *)

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

%K nonn,nice

%O 0,3

%A _N. J. A. Sloane_

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

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Last modified April 12 21:47 EDT 2021. Contains 342933 sequences. (Running on oeis4.)