This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A211564 #7 Jul 19 2018 08:23:21
%S A211564 52,202,813,3046,10096,29503,77078,183074,401337,822277,1590604,
%T A211564 2928879,5168035,8786128,14456683,23108105,35995730,54788196,81669919,
%U A211564 119461564,171760506,243103381,339152932,466911460,634963295,853748807,1135872582
%N A211564 Number of nonnegative integer arrays of length n+4 with new values 0 upwards introduced in order, and containing the value n-1.
%C A211564 Row 5 of A211561.
%H A211564 R. H. Hardin, <a href="/A211564/b211564.txt">Table of n, a(n) for n = 1..210</a>
%F A211564 Empirical: a(n) = (1/384)*n^8 + (1/32)*n^7 + (95/576)*n^6 + (71/120)*n^5 + (2155/1152)*n^4 + (167/32)*n^3 + (3301/288)*n^2 + (2119/120)*n + 15.
%F A211564 Empirical: a(n) = sum{j in n..n+4}stirling2(n+4,j).
%F A211564 Conjectures from _Colin Barker_, Jul 19 2018: (Start)
%F A211564 G.f.: x*(52 - 266*x + 867*x^2 - 1367*x^3 + 1534*x^4 - 1097*x^5 + 497*x^6 - 130*x^7 + 15*x^8) / (1 - x)^9.
%F A211564 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
%F A211564 (End)
%e A211564 Some solutions for n=5:
%e A211564 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A211564 ..1....1....1....1....1....0....1....1....1....1....1....0....1....1....1....1
%e A211564 ..2....1....2....2....2....1....2....2....2....2....2....1....0....2....0....2
%e A211564 ..3....0....3....1....0....2....3....3....2....0....2....0....1....3....2....3
%e A211564 ..4....2....2....0....3....0....4....4....3....1....1....2....2....3....2....0
%e A211564 ..5....3....2....3....4....3....2....4....3....3....3....3....2....2....2....4
%e A211564 ..5....2....1....3....1....4....5....1....4....3....1....3....3....4....3....1
%e A211564 ..4....0....4....4....0....3....0....1....5....4....4....2....0....5....0....0
%e A211564 ..1....4....5....4....2....4....0....1....3....0....0....4....4....6....4....1
%Y A211564 Cf. A211561.
%K A211564 nonn
%O A211564 1,1
%A A211564 _R. H. Hardin_, Apr 15 2012