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 A059203 Number of n-block T_0-covers of a labeled set. 2
 1, 1, 6, 2270, 148109472315, 186266607433353989829111737621541, 7485122439882901107741903784218892557452456923078744798141861944074340339271507786827 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A cover of a set is a T_0-cover if for every two distinct points of the set there exists a member (block) of the cover containing one but not the other point. LINKS FORMULA a(n) = ( - 1)^n + (1/n!)*Sum_{i = 2..n + 1} stirling1(n + 1, i)*floor((2^(i - 1) - 1)!*exp(1)), n>0, a(0) = 1. a(n) = (1/n!)*Sum_{i = 1..n + 1} stirling1(n + 1, i)*A000522(2^(i - 1) - 1). EXAMPLE a(4) = 1 + (1/4!)*( - 50*[1!*e] + 35*[3!*e] - 10*[7!*e] + [15!*e]) = 1 + (1/4!)*( - 50*2 + 35*16 - 10*13700 + 3554627472076) = 148109472315, where [k!*e] := floor(k!*exp(1)). MAPLE with(combinat): Digits := 1500: f := n->(-1)^n+(1/n!)*sum(stirling1(n+1, i)*floor((2^(i-1)-1)!*exp(1)), i=2..n+1): for n from 1 to 10 do printf(`%d, `, f(n)) od: CROSSREFS Cf. A059201, column sums of A059202, A059084 - A059089, A000522. Sequence in context: A051113 A067174 A153300 * A198403 A069643 A067630 Adjacent sequences:  A059200 A059201 A059202 * A059204 A059205 A059206 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Jan 18 2001 EXTENSIONS More terms from James A. Sellers, Jan 24 2001 STATUS approved

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