cp's OEIS Frontend

A211565 Number of nonnegative integer arrays of length n+5 with new values 0 upwards introduced in order, and containing the value n-1.

%I A211565 #7 Nov 20 2014 19:34:43
%S A211565 203,876,4012,17866,72028,256565,810470,2300949,5957407,14253254,
%T A211565 31865787,67190359,134640766,258034213,475437305,845940194,1458930243,
%U A211565 2446555288,4000200734,6391955256,10002207736,15354704197,23160598840
%N A211565 Number of nonnegative integer arrays of length n+5 with new values 0 upwards introduced in order, and containing the value n-1.
%C A211565 Row 6 of A211561.
%H A211565 R. H. Hardin, <a href="/A211565/b211565.txt">Table of n, a(n) for n = 1..210</a>
%F A211565 Empirical: a(n) = (1/3840)*n^10 + (11/2304)*n^9 + (11/288)*n^8 + (1099/5760)*n^7 + (2909/3840)*n^6 + (31511/11520)*n^5 + (3365/384)*n^4 + (66703/2880)*n^3 + (13663/288)*n^2 + (8149/120)*n + 52.
%F A211565 Empirical: a(n) = sum{j in n..n+5} stirling2(n+5,j).
%e A211565 Some solutions for n=5:
%e A211565 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A211565 ..1....1....1....1....1....1....1....1....1....1....0....1....1....1....1....1
%e A211565 ..2....2....2....2....2....2....2....2....2....2....1....2....2....2....2....0
%e A211565 ..2....1....2....3....2....3....1....0....3....3....2....0....1....3....3....1
%e A211565 ..1....3....3....2....1....3....1....3....4....4....3....1....1....4....4....2
%e A211565 ..3....4....4....4....3....4....3....4....1....5....0....3....3....1....2....3
%e A211565 ..4....3....4....4....1....1....3....0....5....6....4....2....3....5....5....1
%e A211565 ..1....1....3....4....2....5....2....3....1....7....5....4....1....0....3....3
%e A211565 ..4....3....5....5....1....4....3....2....3....8....0....4....2....3....1....0
%e A211565 ..3....2....5....5....4....5....4....5....2....2....6....2....4....4....0....4
%Y A211565 Cf. A211561.
%K A211565 nonn
%O A211565 1,1
%A A211565 _R. H. Hardin_, Apr 15 2012