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%I M5287 #27 Sep 20 2017 03:17:00
%S 0,1,45,15913,1073579193,4611686005542975085,
%T 85070591730234615801280047645054636261,
%U 28948022309329048855892746252171976961956366698726387156269151989162886489297
%N Number of proper covers of an n-set.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A007537/b007537.txt">Table of n, a(n) for n = 1..11</a>
%H A. J. Macula, <a href="http://www.jstor.org/stable/2690690">Covers of a finite set</a>, Math. Mag., 67 (1994), 141-144.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ProperCover.html">Proper Cover.</a>
%F a(n) ~ 2^(2^n)/4. - _Vaclav Kotesovec_, Jul 02 2016
%p A007537 := proc(n) 1/2*sum((-1)^k*binomial(n,k)*2^(2^(n-k)),k=0..n)-2^(2^n)/4 end;
%t Table[1/2 Sum[(-1)^k Binomial[n,k]2^(2^(n-k)),{k,0,n}]-2^2^n/4,{n,8}] (* _Harvey P. Dale_, Oct 31 2011 *)
%Y Cf. A003465.
%K nonn,easy,nice
%O 1,3
%A _N. J. A. Sloane_, _Simon Plouffe_
%E One more term from _Emeric Deutsch_, Aug 01 2005
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