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A252873 Number of n X 5 nonnegative integer arrays with upper left 0 and lower right n+5-4 and value increasing by 0 or 1 with every step right or down.

%I A252873 #9 Nov 22 2015 13:19:29
%S A252873 6,61,413,1953,7313,23203,64920,164399,383735,836797,1722394,3373453,
%T A252873 6327844,11427851,19956855,33823579,55806260,89871373,141584051,
%U A252873 218630137,331472883,494170691,725385986,1049619335,1498707293
%N A252873 Number of n X 5 nonnegative integer arrays with upper left 0 and lower right n+5-4 and value increasing by 0 or 1 with every step right or down.
%C A252873 Column 5 of A252876.
%H A252873 R. H. Hardin, <a href="/A252873/b252873.txt">Table of n, a(n) for n = 1..210</a>
%F A252873 Empirical: a(n) = (1/259200)*n^10 + (1/6480)*n^9 + (149/60480)*n^8 + (163/7560)*n^7 + (10411/86400)*n^6 + (1027/2160)*n^5 + (16357/12960)*n^4 + (937/810)*n^3 + (1756/1575)*n^2 - (727/630)*n + 3.
%F A252873 Empirical: G.f.: -x*(6 -5*x +72*x^2 -225*x^3 +460*x^4 -612*x^5 +537*x^6 -315*x^7 +121*x^8 -28*x^9 +3*x^10) / (x-1)^11. - _R. J. Mathar_, Nov 21 2015
%e A252873 Some solutions for n=3:
%e A252873 ..0..1..2..3..4....0..0..0..1..2....0..1..1..1..2....0..0..1..1..2
%e A252873 ..1..2..2..3..4....0..0..1..2..3....0..1..2..2..3....1..1..1..2..3
%e A252873 ..2..3..3..4..4....0..1..2..3..4....1..2..3..3..4....1..1..2..3..4
%K A252873 nonn
%O A252873 1,1
%A A252873 _R. H. Hardin_, Dec 24 2014