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A212930 T(n,k) = number of n X k 0..k-1 arrays with no column j greater than column j-1 in all rows.

%I A212930 #11 Jul 04 2025 19:21:40
%S A212930 1,3,1,10,15,1,35,568,63,1,126,39695,18226,255,1,462,4431876,14177855,
%T A212930 518320,1023,1,1716,724082352,23124921876,4041974015,14230810,4095,1,
%U A212930 6435,163050236504,68264066143602,85800824609376,1075113010175,386357608
%N A212930 T(n,k) = number of n X k 0..k-1 arrays with no column j greater than column j-1 in all rows.
%C A212930 Table starts
%C A212930 .1....3.......10............35................126......................462
%C A212930 .1...15......568.........39695............4431876................724082352
%C A212930 .1...63....18226......14177855........23124921876...........68264066143602
%C A212930 .1..255...518320....4041974015.....85800824609376......4051316109991426752
%C A212930 .1.1023.14230810.1075113010175.285912852294921876.207406617181155352354002
%H A212930 R. H. Hardin, <a href="/A212930/b212930.txt">Table of n, a(n) for n = 1..172</a>
%F A212930 Empirical for column k:
%F A212930 k=1: a(n) = a(n-1)
%F A212930 k=2: a(n) = 5*a(n-1) -4*a(n-2)
%F A212930 k=3: a(n) = 37*a(n-1) -279*a(n-2) +243*a(n-3)
%F A212930 k=4: a(n) = 405*a(n-1) -43860*a(n-2) +1524160*a(n-3) -15636480*a(n-4) +14155776*a(n-5)
%F A212930 The coefficient of a(n-1) is A209671(k) (through at least k=1..7)
%e A212930 Some solutions for n=3 k=4
%e A212930 ..2..0..1..0....1..0..0..0....3..1..1..1....1..0..2..3....2..2..1..0
%e A212930 ..2..0..1..2....0..3..1..2....3..2..3..0....2..1..1..0....0..3..0..0
%e A212930 ..1..3..0..0....1..0..1..3....1..1..1..1....3..3..0..1....1..1..1..3
%Y A212930 Column 2 is A024036.
%Y A212930 Row 1 is A001700(n-1).
%Y A212930 Cf. A212943.
%K A212930 nonn,tabl
%O A212930 1,2
%A A212930 _R. H. Hardin_, May 31 2012