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Array T(n,k) (n >= 1, k >= 1) read by antidiagonals, giving number of ways of arranging the numbers 1 ... mn into an m X n array so there is exactly one local maximum.
13

%I #5 Mar 31 2012 12:35:00

%S 1,2,2,4,16,4,8,208,208,8,16,3584,29568,3584,16,32,76544,7452704,

%T 7452704,76544,32,64,1947648,2941306368,35704394880,2941306368,

%U 1947648,64,128,57477120,1683453629440,331333877743200,331333877743200,1683453629440,57477120,128,256,1929117696,1323082429842432,5338455334819710720,88366736882654697600,5338455334819710720,1323082429842432,1929117696,256,512,72545402880,1370418864769445888,137813651152462288749440

%N Array T(n,k) (n >= 1, k >= 1) read by antidiagonals, giving number of ways of arranging the numbers 1 ... mn into an m X n array so there is exactly one local maximum.

%F T(n, k) = T(k, n). T(n, 1) = 2^(n-1) (see A000079).

%e Array begins:

%e 1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,...

%e 2,16,208,3584,76544,1947648,57477120,1929117696...

%e 4,208,29568,7452704,2941306368,1683453629440...

%e 8,3584,7452704,35704394880,331333877743200,...

%e 16,76544,2941306368,331333877743200,...

%Y Cf. A000079 (k = 1 or n = 1), A087518 (n=k). A087923-A087932 give rows 2 through 11. Cf. A007846.

%K nonn,tabl,nice

%O 1,2

%A _R. H. Hardin_, Oct 25 2003