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 A281547 Total number of subsets of X that are both open and closed summed over all distinct topological spaces X that can be placed on an n-set. 1
 1, 2, 10, 82, 1038, 19754, 561778, 23890766, 1516425978, 142478603490, 19560464078774, 3868751287074546, 1088233853378616578, 430599111941369628326, 237480490462200909980594, 181131722604060126010422898, 189780362331001773747253412782, 271553393666987988551182068682458, 527932854364810523962111033565618786 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Wikipedia, Clopen set. FORMULA E.g.f.: A(exp(x) - 1)^2 where A(x) is the e.g.f. for A001035. a(n) = Sum_{k=1..n} A247232(n,k)*2^k. EXAMPLE a(2) = 10.  Let X = {a,b}.  There are four distinct topologies (A000798) that can be placed on X: {{},X}  {{},{a},X}  {{}, {b},X}  {{},{a},{b},X}.  These topologies have 2 + 2 + 2 + 4 sets respectively that are both open and closed. CROSSREFS Cf. A000798, A001035, A247232. Sequence in context: A321089 A112487 A089469 * A111265 A296667 A003093 Adjacent sequences:  A281544 A281545 A281546 * A281548 A281549 A281550 KEYWORD nonn AUTHOR Geoffrey Critzer, Jan 23 2017 STATUS approved

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Last modified August 24 22:41 EDT 2019. Contains 326314 sequences. (Running on oeis4.)