This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A281780 #19 Sep 07 2024 09:14:03 %S A281780 0,0,0,0,12,660,20400,445620,7977732,126860580,1873839000,26381789940, %T A281780 359484471852,4784481401700,62538498859200,805447464281460, %U A281780 10241415118476372,128722997969290020,1600670708273985000,19705915838479512180,240330009637668935292 %N A281780 Number of distinct topologies on an n-set that have exactly 12 open sets. %H A281780 Ray Chandler, <a href="/A281780/b281780.txt">Table of n, a(n) for n = 0..960</a> %H A281780 Moussa Benoumhani, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Benoumhani/benoumhani11.html">The Number of Topologies on a Finite Set</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.6. %H A281780 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (66, -1925, 32670, -357423, 2637558, -13339535, 45995730, -105258076, 150917976, -120543840, 39916800). %F A281780 a(n) = 1/2*4! Stirling2(n, 4) + 9/2*5! Stirling2(n, 5) + 16*6! Stirling2(n, 6) + 295/12*7! Stirling2(n, 7) + 85/4*8! Stirling2(n, 8) + 49/4*9! Stirling2(n, 9) + 9/2*10! Stirling2(n, 10) + 11!*Stirling2(n, 11). %Y A281780 The number of distinct topologies on an n-set with exactly k open sets for k=2..12 is given by A000012, A000918, A281773, A028244, A281774, A281775, A281776, A281777, A281778, A281779, A281780. %K A281780 nonn %O A281780 0,5 %A A281780 _Geoffrey Critzer_, Jan 29 2017