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A211566 Number of nonnegative integer arrays of length n+6 with new values 0 upwards introduced in order, and containing the value n-1.

%I A211566 #6 Jun 02 2025 07:47:45
%S A211566 877,4139,20891,106133,503295,2134122,8016373,26869727,81381744,
%T A211566 225620777,579251337,1390969632,3150473373,6777961885,13933402774,
%U A211566 27505504247,52363544091,96485126179,172610924931,300625072411
%N A211566 Number of nonnegative integer arrays of length n+6 with new values 0 upwards introduced in order, and containing the value n-1.
%C A211566 Row 7 of A211561
%H A211566 R. H. Hardin, <a href="/A211566/b211566.txt">Table of n, a(n) for n = 1..210</a>
%F A211566 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 A211566 Empirical: a(n) = sum{j in n..n+6}stirling2(n+6,j)
%e A211566 Some solutions for n=5
%e A211566 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A211566 ..1....0....1....0....0....0....0....1....0....1....1....0....0....1....0....0
%e A211566 ..0....1....0....1....1....1....1....0....0....0....0....1....1....0....1....1
%e A211566 ..1....2....2....2....2....2....1....2....0....2....1....2....2....2....2....0
%e A211566 ..2....3....0....1....3....3....2....1....1....0....2....0....1....1....2....1
%e A211566 ..3....3....0....0....0....2....3....2....2....3....3....2....3....2....3....2
%e A211566 ..4....1....2....1....2....4....1....3....2....3....2....3....1....1....4....2
%e A211566 ..5....0....1....3....4....5....3....2....3....0....1....3....4....3....1....3
%e A211566 ..0....1....0....2....1....3....0....4....1....3....4....4....2....2....2....4
%e A211566 ..0....4....3....4....5....0....4....3....3....4....5....5....4....4....1....0
%e A211566 ..4....1....4....1....5....5....5....0....4....2....6....6....0....0....4....3
%K A211566 nonn
%O A211566 1,1
%A A211566 _R. H. Hardin_ Apr 15 2012