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Number of nonnegative integer arrays of length n+6 with new values 0 upwards introduced in order, and containing the value n-1
1

%I #4 Apr 15 2012 18:07:27

%S 877,4139,20891,106133,503295,2134122,8016373,26869727,81381744,

%T 225620777,579251337,1390969632,3150473373,6777961885,13933402774,

%U 27505504247,52363544091,96485126179,172610924931,300625072411

%N Number of nonnegative integer arrays of length n+6 with new values 0 upwards introduced in order, and containing the value n-1

%C Row 7 of A211561

%H R. H. Hardin, <a href="/A211566/b211566.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/46080)*n^12 + (13/23040)*n^11 + (33/5120)*n^10 + (9241/207360)*n^9 + (10423/46080)*n^8 + (478007/483840)*n^7 + (61073/15360)*n^6 + (197717/13824)*n^5 + (504739/11520)*n^4 + (1139725/10368)*n^3 + (102469/480)*n^2 + (361919/1260)*n + 203

%F Empirical: a(n) = sum{j in n..n+6}stirling2(n+6,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....0....1....0....0....0....0....1....0....1....1....0....0....1....0....0

%e ..0....1....0....1....1....1....1....0....0....0....0....1....1....0....1....1

%e ..1....2....2....2....2....2....1....2....0....2....1....2....2....2....2....0

%e ..2....3....0....1....3....3....2....1....1....0....2....0....1....1....2....1

%e ..3....3....0....0....0....2....3....2....2....3....3....2....3....2....3....2

%e ..4....1....2....1....2....4....1....3....2....3....2....3....1....1....4....2

%e ..5....0....1....3....4....5....3....2....3....0....1....3....4....3....1....3

%e ..0....1....0....2....1....3....0....4....1....3....4....4....2....2....2....4

%e ..0....4....3....4....5....0....4....3....3....4....5....5....4....4....1....0

%e ..4....1....4....1....5....5....5....0....4....2....6....6....0....0....4....3

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 15 2012