login
A281780
Number of distinct topologies on an n-set that have exactly 12 open sets.
8
0, 0, 0, 0, 12, 660, 20400, 445620, 7977732, 126860580, 1873839000, 26381789940, 359484471852, 4784481401700, 62538498859200, 805447464281460, 10241415118476372, 128722997969290020, 1600670708273985000, 19705915838479512180, 240330009637668935292
OFFSET
0,5
LINKS
Moussa Benoumhani, The Number of Topologies on a Finite Set, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.6.
Index entries for linear recurrences with constant coefficients, signature (66, -1925, 32670, -357423, 2637558, -13339535, 45995730, -105258076, 150917976, -120543840, 39916800).
FORMULA
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).
CROSSREFS
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.
Sequence in context: A195574 A195554 A220327 * A295870 A177322 A060612
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jan 29 2017
STATUS
approved