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A281547
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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.
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1
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1, 2, 10, 82, 1038, 19754, 561778, 23890766, 1516425978, 142478603490, 19560464078774, 3868751287074546, 1088233853378616578, 430599111941369628326, 237480490462200909980594, 181131722604060126010422898, 189780362331001773747253412782, 271553393666987988551182068682458, 527932854364810523962111033565618786
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OFFSET
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0,2
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LINKS
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FORMULA
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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.
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EXAMPLE
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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.
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MATHEMATICA
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A001035 = Cases[Import["https://oeis.org/A001035/b001035.txt", "Table"], {_, _}][[All, 2]];
A[x_] = Sum[A001035[[n + 1]] x^n/n!, {n, 0, lg - 1}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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