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%I #23 Feb 25 2016 03:13:28
%S 1,2,12,4,74,1442,8,456,28028,1716098,16,2810,544844,105093828,
%T 20276816980,32,17316,10591310,6435880414,3912156203494,
%U 2378025136264102,64,106706,205886234,394129505248,754801786191820,1445496758320387318,2768227968406304217000,128,657552,4002256640,24136256828880
%N Triangle read by rows: T(n,k) is the number of ways to partition an n X k square grid into any number of parts along the gridlines.
%C A set of edges forms a valid partition if and only if it includes the entire boundary of the grid, and there are no vertices of degree 1.
%H Danny Rorabaugh, <a href="/A264841/a264841.pdf">A264841 Example: T(2,2)</a>
%H R. J. Mathar, <a href="http://www.vixra.org/abs/1511.0225">Counting 2-way monotonic terrace forms over rectangular landscapes</a>, see Section 6.3, Combinatorics and Graph Theory, viXra:1511.0225, 2015.
%F T(n,1) = 2^(n-1).
%F T(n,2) = A078469(n).
%e The triangle T(n,k) begins:
%e n\k 1 2 3 4 5
%e 1: 1
%e 2: 2 12
%e 3: 4 74 1442
%e 4: 8 456 28028 1716098
%e 5: 16 2810 544844 105093828 20276816980
%Y A078469 is the second column of this triangle.
%K nonn,tabl
%O 1,2
%A _Linus Hamilton_, Nov 26 2015
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