|
%I #10 Dec 28 2016 17:31:17
%S 1,1,6,2270,148109472315,186266607433353989829111737621541,
%T 7485122439882901107741903784218892557452456923078744798141861944074340339271507786827
%N Number of n-block T_0-covers of a labeled set.
%C 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.
%H G. C. Greubel, <a href="/A059203/b059203.txt">Table of n, a(n) for n = 0..8</a>
%F 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.
%F a(n) = (1/n!)*Sum_{i = 1,..,n + 1} stirling1(n + 1, i)*A000522(2^(i - 1) - 1).
%e 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)).
%p 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:
%t 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 *)
%Y Cf. A059201, column sums of A059202, A059084 - A059089, A000522.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Goran Kilibarda, Jan 18 2001
%E More terms from _James A. Sellers_, Jan 24 2001
|
