%I #4 Apr 15 2012 17:58:42
%S 1,11,81,512,3046,17866,106133,649045,4125023,27378716,190102160,
%T 1380567060,10472967693,82843346443,682012236077,5832548494812,
%U 51723577104638,474868072764550,4506710508270721,44151990164554541
%N Number of nonnegative integer arrays of length n+3 with new values 0 upwards introduced in order, and containing the value 3
%C Column 4 of A211561
%H R. H. Hardin, <a href="/A211557/b211557.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = sum{j in 4..n+3}stirling2(n+3,j)
%e Some solutions for n=5
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....1....0....1....1....0....1....1....1....0....1....1....1....1....1....1
%e ..0....0....0....2....2....1....2....2....1....1....2....2....1....2....2....0
%e ..2....2....1....3....3....2....0....0....2....2....0....0....2....3....0....2
%e ..0....1....2....0....1....0....3....2....2....2....3....0....3....2....3....3
%e ..2....0....1....1....3....1....1....3....3....3....4....1....1....2....2....2
%e ..3....2....3....4....4....0....0....2....0....0....2....0....2....1....3....0
%e ..0....3....0....4....2....3....1....3....4....1....3....3....0....0....2....3
%K nonn
%O 1,2
%A _R. H. Hardin_ Apr 15 2012
