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A252927 Number of nX5 nonnegative integer arrays with upper left 0 and lower right n+5-6 and value increasing by 0 or 1 with every step right or down.

%I A252927 #8 Jul 23 2025 13:46:16
%S A252927 1,19,413,6997,84910,762227,5385305,31454256,157376166,692347393,
%T A252927 2731553014,9814551889,32510650689,100275435009,290361386801,
%U A252927 794754882094,2068183070502,5142171510385,12267196687798,28182388823719
%N A252927 Number of nX5 nonnegative integer arrays with upper left 0 and lower right n+5-6 and value increasing by 0 or 1 with every step right or down.
%C A252927 Column 5 of A252930
%H A252927 R. H. Hardin, <a href="/A252927/b252927.txt">Table of n, a(n) for n = 1..210</a>
%F A252927 Empirical: a(n) = (47/17888985354240000)*n^20 + (47/149074877952000)*n^19 + (167/10003708915200)*n^18 + (4591/8892185702400)*n^17 + (29063/2802159360000)*n^16 + (187361/1307674368000)*n^15 + (13481939/9415255449600)*n^14 + (1082533/98075577600)*n^13 + (454942751/6584094720000)*n^12 + (23035147/67060224000)*n^11 + (43650403/34488115200)*n^10 + (134989213/40236134400)*n^9 + (2353290548929/470762772480000)*n^8 - (1781952749/3923023104000)*n^7 + (174219179149/2353813862400)*n^6 + (1662462491/16345929600)*n^5 + (42818968289/66718080000)*n^4 - (16827599/22422400)*n^3 + (9481442611/5333065920)*n^2 - (565043267/116396280)*n + 4.
%F A252927 Empirical: G.f.: -x*(1 -2*x +224*x^2 +984*x^3 +5418*x^4 -7437*x^5 +43066*x^6 -112135*x^7 +198529*x^8 -285030*x^9 +339839*x^10 -332484*x^11 +266120*x^12 -174781*x^13 +93817*x^14 -40498*x^15 +13679*x^16 -3477*x^17 +627*x^18 -72*x^19 +4*x^20) / (x-1)^21 . - _R. J. Mathar_, Nov 24 2015
%e A252927 Some solutions for n=4
%e A252927 ..0..1..1..1..2....0..1..1..1..1....0..0..1..2..3....0..0..0..1..1
%e A252927 ..0..1..1..2..2....0..1..2..2..2....0..0..1..2..3....0..1..1..1..2
%e A252927 ..0..1..1..2..2....1..1..2..2..2....1..1..2..3..3....0..1..2..2..3
%e A252927 ..1..1..1..2..3....2..2..2..2..3....1..1..2..3..3....1..1..2..2..3
%K A252927 nonn
%O A252927 1,2
%A A252927 _R. H. Hardin_, Dec 24 2014