A281780 Number of distinct topologies on an n-set that have exactly 12 open sets.

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

Table of n, a(n) for n=0..20.

Moussa Benoumhani, The Number of Topologies on a Finite Set, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.6.

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

Adjacent sequences: A281777 A281778 A281779 * A281781 A281782 A281783

Keyword

nonn

Author

Geoffrey Critzer, Jan 29 2017

Status

approved