%I A052655
%S A052655 0,1,6,18,96,600,4320,35280,322560,3265920,36288000,439084800,
%T A052655 5748019200,80951270400,1220496076800,19615115520000,334764638208000,
%U A052655 6046686277632000,115242726703104000,2311256907767808000
%N A052655 a(2) = 6, otherwise a(n) = n*n!.
%C A052655 A simple regular expression in a labeled universe.
%C A052655 a(n) = number of real non-singular (0,1)-matrices of order n having maximal 
               permanent = A000255(n). Proof: [W. Edwin Clark and Richard Brualdi] 
               The maximum permanent is per A where A has all 1's except for n-1 
               0's on the main diagonal. By Corollary 4.4 in the Brualdi et al. 
               reference for n >= 4 any n X n (0,1)-matrix B with per B = per A 
               can be obtained from A by permuting rows and columns. Since there 
               are n ways to place the single 1 on the main diagonal and then n! 
               ways to permute the distinct rows, a(n) = n*n! if n >=4. Direct computation 
               shows this also holds for n = 1 and 3. - W. Edwin Clark (eclark(AT)math.usf.edu), 
               Nov 15 2003
%D A052655 Brualdi, Richard A.; Goldwasser, John L.; and Michael, T. S., Maximum 
               permanents of matrices of zeros and ones. J. Combin. Theory Ser. 
               A 47 (1988), 207-245.
%H A052655 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=602">
               Encyclopedia of Combinatorial Structures 602</a>
%F A052655 E.g.f.: x*(-2*x^2+x^3+x+1)/(-1+x)^2
%e A052655 a(2)=6 because there are 6 (0,1)-matrices with nonzero determinant having 
               permanent=1. See example in A089482. The (0,1)-matrix with maximal 
               permanent=2 ((1,1),(1,1)) has det=0.
%p A052655 spec := [S,{S=Prod(Z,Union(Z,Prod(Sequence(Z),Sequence(Z))))},labeled]: 
               seq(combstruct[count](spec,size=n), n=0..20);
%Y A052655 Cf. A000255. A089480 gives occurrence counts for permanents of non-singular 
               (0, 1)-matrices, A051752 number of (0, 1)-matrices with maximal determinant 
               A003432.
%Y A052655 Essentially the same as A001563.
%Y A052655 Sequence in context: A104970 A151470 A009573 this_sequence A108735 A143556 
               A007126
%Y A052655 Adjacent sequences: A052652 A052653 A052654 this_sequence A052656 A052657 
               A052658
%K A052655 easy,nonn
%O A052655 0,3
%A A052655 encyclopedia(AT)pommard.inria.fr, Jan 25 2000