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%I #4 Dec 29 2015 10:16:26
%S 6,34,212,1391,8764,49894,251381,1122721,4490732,16284683,54165714,
%T 166968275,481237398,1306708520,3364174219,8257222586,19412425379,
%U 43890267973,95767324137,202278568268,414691101885,827108931171
%N Number of 5Xn binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.
%C Row 5 of A266428.
%H R. H. Hardin, <a href="/A266431/b266431.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/7602818775552000)*n^19 + (1/47076277248000)*n^18 + (389/266765571072000)*n^17 + (47/815173632000)*n^16 + (11629/7846046208000)*n^15 + (413249/15692092416000)*n^14 + (7941701/23538138624000)*n^13 + (23266079/7242504192000)*n^12 + (14091433/603542016000)*n^11 + (267047/1959552000)*n^10 + (794703337/1207084032000)*n^9 + (14650018639/4828336128000)*n^8 + (267287875667/23538138624000)*n^7 + (102484112767/2139830784000)*n^6 + (39001810891/326918592000)*n^5 + (73310538271/186810624000)*n^4 + (87546462023/102918816000)*n^3 + (113077535/72648576)*n^2 + (469781209/232792560)*n + 1
%e Some solutions for n=4
%e ..0..0..1..1....0..1..1..1....0..0..1..1....0..0..0..1....0..0..0..1
%e ..0..0..1..1....0..1..1..1....0..1..0..1....0..0..1..1....0..0..1..0
%e ..0..0..1..1....0..1..1..1....1..0..1..0....0..1..1..1....0..0..1..1
%e ..0..1..0..0....1..1..1..1....1..1..0..0....1..0..1..1....0..1..1..1
%e ..1..1..0..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..0..1
%Y Cf. A266428.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 29 2015
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