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%I #8 Jun 01 2018 11:57:32
%S 1,5,31,184,924,3809,13197,39675,106357,259669,586829,1242946,2491516,
%T 4763097,8738111,15461061,26494977,44126629,71634979,113637500,
%U 176531380,269049265,402952089,593884703,862423461,1235348661,1747178785
%N Number of n X 5 nonnegative integer arrays with each row and column increasing from zero by 0 or 1.
%C Column 5 of A202756.
%H R. H. Hardin, <a href="/A202753/b202753.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/302400)*n^10 + (1/10080)*n^9 + (1/1008)*n^8 + (1/336)*n^7 - (67/14400)*n^6 + (7/480)*n^5 + (1021/6048)*n^4 - (145/1008)*n^3 + (10519/12600)*n^2 - (367/420)*n + 1.
%F Conjectures from _Colin Barker_, Jun 01 2018: (Start)
%F G.f.: x*(1 - 6*x + 31*x^2 - 47*x^3 + 110*x^4 - 162*x^5 + 140*x^6 - 79*x^7 + 31*x^8 - 8*x^9 + x^10) / (1 - x)^11.
%F a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
%F (End)
%e Some solutions for n=5:
%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e ..0..1..1..1..1....0..0..0..0..0....0..0..1..1..1....0..0..0..0..1
%e ..0..1..1..1..2....0..0..0..1..1....0..1..1..1..1....0..0..0..0..1
%e ..0..1..1..2..3....0..0..0..1..2....0..1..1..2..2....0..1..1..1..1
%e ..0..1..2..3..4....0..0..1..1..2....0..1..2..2..2....0..1..1..2..2
%Y Cf. A202756.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 23 2011
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