

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.


13



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
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OFFSET

1,2


LINKS

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


FORMULA

T(n, k) = T(k, n). T(n, 1) = 2^(n1) (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). A087923A087932 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



