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A281776 Number of distinct topologies on an n-set that have exactly 8 open sets. 8
0, 0, 0, 1, 54, 955, 11760, 122941, 1175034, 10595215, 91506420, 763624081, 6194818014, 49084747075, 381338401080, 2914184784421, 21965095364994, 163656285828535, 1207613518375740, 8838842878371961, 64253768864671974, 464416229729871595, 3340518964319750400 (list; graph; refs; listen; history; text; internal format)
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 (28,-322,1960,-6769,13132,-13068,5040).

FORMULA

a(n) = StirlingS2(n, 3) + 2*4! StirlingS2(n, 4) + 15/4*5! StirlingS2(n, 5) + 5/2*6! StirlingS2(n, 6) + 7! StirlingS2(n, 7).

From Colin Barker, Jan 30 2017: (Start)

a(n) = 13/4 - 19*2^(n-1) + 44*3^(n-1) - 2^(n-1)*3^(2+n) - 57*4^(n-1) + (39*5^n)/4 + 7^n for n>0.

G.f.: x^3*(1 + 26*x - 235*x^2 + 448*x^3 + 2100*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)).

(End)

PROG

(PARI) concat(vector(3), Vec(x^3*(1 + 26*x - 235*x^2 + 448*x^3 + 2100*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*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: A280479 A107420 A298069 * A160345 A298718 A245832

Adjacent sequences:  A281773 A281774 A281775 * A281777 A281778 A281779

KEYWORD

nonn,easy

AUTHOR

Geoffrey Critzer, Jan 29 2017

STATUS

approved

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Last modified April 26 09:52 EDT 2019. Contains 322472 sequences. (Running on oeis4.)