%I #7 Dec 05 2016 02:41:52

%S 1,1,1,1,1,1,1,1,2,1,1,1,2,3,1,1,1,2,4,4,1,1,1,2,4,6,6,1,1,1,2,4,7,11,

%T 8,1,1,1,2,4,7,13,19,12,1,1,1,2,4,7,14,25,33,16,1,1,1,2,4,7,14,27,49,

%U 55,22,1,1,1,2,4,7,14,28,55,93,95,29,1,1,1,2,4,7,14,28,57,111,181,158,40,1

%N Table by antidiagonals: a(m,n) is the number of m-dimensional partitions of n up to conjugacy, for m >= 0, n >= 1.

%C Partitions are considered as generalized Ferrers diagrams; any permutation of the axes produces a conjugate.

%e Table starts:

%e 1, 1, 1, 1, 1, 1, ...

%e 1, 1, 2, 3, 4, 6, ...

%e 1, 1, 2, 4, 6, 11, ...

%e 1, 1, 2, 4, 7, 13, ...

%e 1, 1, 2, 4, 7, 14, ...

%e ...

%Y Rows: A000012, A046682, A000786, A119266, A119267, A119340, A119341, A119342 stabilize to A119268. Transposed table is A119269. Cf. A119339, A119270, A118364, A118365.

%K nonn,tabl

%O 1,9

%A _Max Alekseyev_, May 15 2006