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A202549 T(n,k) = Number of n X k nonnegative integer arrays with each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).

%I A202549 #7 May 09 2022 00:41:22
%S A202549 1,1,1,1,2,1,1,4,4,1,1,8,18,8,1,1,16,86,86,16,1,1,32,422,1094,422,32,
%T A202549 1,1,64,2094,15184,15184,2094,64,1,1,128,10438,219934,658492,219934,
%U A202549 10438,128,1,1,256,52126,3249298,31670778,31670778,3249298,52126,256,1,1,512
%N A202549 T(n,k) = Number of n X k nonnegative integer arrays with each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it).
%C A202549 Table starts
%C A202549 .1...1.....1........1...........1...............1..................1
%C A202549 .1...2.....4........8..........16..............32.................64
%C A202549 .1...4....18.......86.........422............2094..............10438
%C A202549 .1...8....86.....1094.......15184..........219934............3249298
%C A202549 .1..16...422....15184......658492........31670778.........1605067272
%C A202549 .1..32..2094...219934....31670778......5534917394......1078490778110
%C A202549 .1..64.10438..3249298..1605067272...1078490778110....876480920594230
%C A202549 .1.128.52126.48427802.83391232150.222425177005132.794166642153146254
%H A202549 R. H. Hardin, <a href="/A202549/b202549.txt">Table of n, a(n) for n = 1..144</a>
%e A202549 Some solutions for n=4, k=4
%e A202549 ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e A202549 ..0..1..1..1....0..1..1..0....0..0..1..1....0..1..1..0....0..1..0..1
%e A202549 ..0..1..1..0....0..0..1..0....0..0..1..0....0..0..1..1....0..0..0..1
%e A202549 ..0..1..2..0....0..1..2..1....0..0..1..1....0..1..1..1....0..1..1..2
%Y A202549 Column 2 is A000079(n-1).
%Y A202549 Column 3 is A082685(n-1).
%K A202549 nonn,tabl
%O A202549 1,5
%A A202549 _R. H. Hardin_, Dec 20 2011