A281780 - OEIS

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

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OFFSET

0,5

LINKS

Ray Chandler, Table of n, a(n) for n = 0..960

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

Adjacent sequences: A281777 A281778 A281779 * A281781 A281782 A281783

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jan 29 2017

STATUS

approved