A087783 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.

1, 2, 2, 4, 16, 4, 8, 208, 208, 8, 16, 3584, 29568, 3584, 16, 32, 76544, 7452704, 7452704, 76544, 32, 64, 1947648, 2941306368, 35704394880, 2941306368, 1947648, 64, 128, 57477120, 1683453629440, 331333877743200, 331333877743200, 1683453629440, 57477120, 128, 256, 1929117696, 1323082429842432, 5338455334819710720, 88366736882654697600, 5338455334819710720, 1323082429842432, 1929117696, 256, 512, 72545402880, 1370418864769445888, 137813651152462288749440

Offset

1,2

Links

Table of n, a(n) for n=1..49.

Formula

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

Example

Array begins:
1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,...
2,16,208,3584,76544,1947648,57477120,1929117696...
4,208,29568,7452704,2941306368,1683453629440...
8,3584,7452704,35704394880,331333877743200,...
16,76544,2941306368,331333877743200,...

Crossrefs

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

Sequence in context: A122598 A279069 A257609 * A176190 A106241 A153991

Adjacent sequences: A087780 A087781 A087782 * A087784 A087785 A087786

Keyword

nonn,tabl,nice

Author

R. H. Hardin, Oct 25 2003

Status

approved