A059203 Number of n-block T_0-covers of a labeled set.

1, 1, 6, 2270, 148109472315, 186266607433353989829111737621541, 7485122439882901107741903784218892557452456923078744798141861944074340339271507786827

Offset: 0

Author

Vladeta Jovovic, Goran Kilibarda, Jan 18 2001

Keywords

• easy
• nonn

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.

Examples

			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)).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..8

Crossrefs

Cf. A059201, column sums of A059202, A059084 - A059089, A000522.

Programs

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:

Mathematica

a[0] := 1; a[n_] := (-1)^n + (1/n!)*Sum[StirlingS1[n + 1, k]*Floor[(2^(k - 1) - 1)!*E], {k, 2, n + 1}]; Table[a[n], {n, 0, 5}] (* G. C. Greubel, Dec 28 2016 *)

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).

Extensions

More terms from James Sellers, Jan 24 2001