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Number of proper T_0-covers of an n-set.
2

%I #9 May 10 2013 12:45:34

%S 0,1,42,15654,1073421588,4611685989440629944,

%T 85070591730234615704434641716516893512,

%U 28948022309329048855892746252171976959574390130279817915318273546782086570304

%N Number of proper T_0-covers of an n-set.

%C The next term has 154 decimal digits.

%F a(n) = Sum(Stirling1(n, k)*A007537(k), k=1..n).

%F a(n) = Sum((2*Stirling1(n+1, k+1)-Stirling1(n, k))*2^(2^k-2), k=0..n).

%o (PARI)

%o a(n)=sum(k=0,n, (2*stirling(n+1, k+1, 1) - stirling(n, k,1 )) * 2^(2^k-2) );

%o vector(10,n,a(n)) /* show terms */

%Y Row sums of A095422, A095421.

%K easy,nonn

%O 1,3

%A Goran Kilibarda, _Vladeta Jovovic_, Jun 04 2004