A281777 - OEIS

A281777

Number of distinct topologies on an n-set that have exactly 9 open sets.

0, 0, 0, 0, 20, 800, 14260, 189280, 2181060, 23241120, 235737620, 2308206560, 21979728100, 204477713440, 1864504348980, 16707856095840, 147469451067140, 1284607771225760, 11063319237792340, 94343562846289120, 797685042851814180, 6694943490279586080

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OFFSET

0,5

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

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 (36,-546,4536,-22449,67284,-118124,109584,-40320).

FORMULA

a(n) = 5/6*4! Stirling2(n, 4) + 5*5! Stirling2(n, 5) + 11/2*6! Stirling2(n, 6) + 3*7! Stirling2(n, 7) + 8! Stirling2(n, 8).

G.f.: 20*x^4*(1 + 4*x - 181*x^2 + 1100*x^3 - 1344*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)). - Colin Barker, Jan 30 2017

MATHEMATICA

LinearRecurrence[{36, -546, 4536, -22449, 67284, -118124, 109584, -40320}, {0, 0, 0, 0, 20, 800, 14260, 189280, 2181060}, 30] (* Harvey P. Dale, Aug 19 2020 *)

PROG

(PARI) concat(vector(4), Vec(20*x^4*(1 + 4*x - 181*x^2 + 1100*x^3 - 1344*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)*(1 - 8*x)) + O(x^30))) \\ Colin Barker, Jan 30 2017

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: A002455 A322890 A267671 * A041763 A041760 A250550

Adjacent sequences: A281774 A281775 A281776 * A281778 A281779 A281780

KEYWORD

nonn,easy

AUTHOR

Submitted on behalf of Moussa Benoumhani by Geoffrey Critzer, Jan 29 2017

STATUS

approved