cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A334252 Number of closure operators on a set of n elements which satisfy the T_0 separation axiom.

Original entry on oeis.org

1, 2, 5, 44, 2179, 1362585, 75953166947, 14087646640499308474
Offset: 0

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Author

Joshua Moerman, Apr 20 2020

Keywords

Comments

The T_0 axiom states that the closure of {x} and {y} are different for distinct x and y.

Examples

			The a(0) = 1 through a(2) = 5 set-systems of closed sets:
{{}}  {{}}      {{1,2},{1}}
      {{1},{}}  {{1,2},{2}}
                {{1,2},{1},{}}
                {{1,2},{2},{}}
                {{1,2},{1},{2},{}}
		

Crossrefs

The number of all closure operators is given in A102896.
For strict T0 closure operators, see A334253.
For T1 closure operators, see A334254.

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k) * A102896(k). - Andrew Howroyd, Apr 20 2020

Extensions

a(6)-a(7) from Andrew Howroyd, Apr 20 2020