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A245789 Rectangular array A read by upward antidiagonals: A(k,n) = (2^k-1)^n, n,k >= 1.

%I A245789 #30 Nov 30 2014 15:13:49
%S A245789 1,1,3,1,9,7,1,27,49,15,1,81,343,225,31,1,243,2401,3375,961,63,1,729,
%T A245789 16807,50625,29791,3969,127,1,2187,117649,759375,923521,250047,16129,
%U A245789 255,1,6561,823543,11390625,28629151,15752961,2048383,65025,511
%N A245789 Rectangular array A read by upward antidiagonals: A(k,n) = (2^k-1)^n, n,k >= 1.
%C A245789 A(k,n) is the number of sequences (X_1, X_2, ..., X_k) of subsets of the set {1, 2, ..., n} such that intersect_{j=1..k} X_j = null.
%D A245789 Richard P. Stanley, Enumerative Combinatorics, Cambridge University Press, Vol. 1, Second edition, 2012, p. 14 (Example 1.1.16).
%H A245789 L. Edson Jeffery, <a href="/A245789/b245789.txt">Table of n, a(n) for n = 1..45</a>
%e A245789 Array A begins:
%e A245789 1      3         7           15              31                 63
%e A245789 1      9        49          225             961               3969
%e A245789 1     27       343         3375           29791             250047
%e A245789 1     81      2401        50625          923521           15752961
%e A245789 1    243     16807       759375        28629151          992436543
%e A245789 1    729    117649     11390625       887503681        62523502209
%e A245789 1   2187    823543    170859375     27512614111      3938980639167
%e A245789 1   6561   5764801   2562890625    852891037441    248155780267521
%e A245789 1  19683  40353607  38443359375  26439622160671  15633814156853823
%t A245789 (* Array *)
%t A245789 a[k_, n_] := (2^k - 1)^n; Grid[Table[a[k, n], {n, 12}, {k, 12}]]
%t A245789 (* Array antidiagonals flattened *)
%t A245789 Flatten[Table[(2^k - 1)^(n - k + 1), {n, 12}, {k, n}]]
%Y A245789 Cf. A000225, A060867, A128831, etc. (rows 1-3).
%Y A245789 Cf. A000012, A000244, A000420, etc. (columns 1-3).
%Y A245789 Cf. A055601 (main diagonal).
%K A245789 nonn,tabl
%O A245789 1,3
%A A245789 _L. Edson Jeffery_, Aug 22 2014