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 A052655 a(2) = 6, otherwise a(n) = n*n!. 2
 0, 1, 6, 18, 96, 600, 4320, 35280, 322560, 3265920, 36288000, 439084800, 5748019200, 80951270400, 1220496076800, 19615115520000, 334764638208000, 6046686277632000, 115242726703104000, 2311256907767808000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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, Nov 15 2003 LINKS Table of n, a(n) for n=0..19. Richard A. Brualdi, John L. Goldwasser, T. S. Michael, Maximum permanents of matrices of zeros and ones, J. Combin. Theory Ser. A 47 (1988), 207-245. INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 602 FORMULA E.g.f.: x*(-2*x^2+x^3+x+1)/(-1+x)^2. EXAMPLE 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. MAPLE spec := [S, {S=Prod(Z, Union(Z, Prod(Sequence(Z), Sequence(Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); MATHEMATICA Join[{0, 1, 6}, Table[n*n!, {n, 3, 20}]] (* Harvey P. Dale, Apr 20 2012 *) CROSSREFS Cf. A000255. A089480 gives occurrence counts for permanents of non-singular (0, 1)-matrices, A051752 number of (0, 1)-matrices with maximal determinant A003432. Essentially the same as A001563. Sequence in context: A151470 A280096 A009573 * A274499 A181038 A222857 Adjacent sequences: A052652 A052653 A052654 * A052656 A052657 A052658 KEYWORD easy,nonn AUTHOR encyclopedia(AT)pommard.inria.fr, Jan 25 2000 STATUS approved

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Last modified February 24 11:15 EST 2024. Contains 370303 sequences. (Running on oeis4.)