A202755 - OEIS

%I #5 Mar 31 2012 12:36:51

%S 1,7,78,1022,13197,150777,1442764,11408125,75393424,424992394,

%T 2086954916,9097630767,35775808290,128617512596,427443971156,

%U 1325376633243,3864035126505,10661515466643,27995060608622,70289431296342

%N Number of nX7 nonnegative integer arrays with each row and column increasing from zero by 0 or 1

%C Column 7 of A202756

%H R. H. Hardin, <a href="/A202755/b202755.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/1520925880320000)*n^21 + (1/14485008384000)*n^20 + (17/5431878144000)*n^19 + (41/517321728000)*n^18 + (10847/9053130240000)*n^17 + (73/6897623040)*n^16 + (3646499/76046294016000)*n^15 + (340729/3621252096000)*n^14 + (186024683/217275125760000)*n^13 + (282751/26873856000)*n^12 + (25808261/724250419200)*n^11 + (2895163/86220288000)*n^10 + (493582091273/760462940160000)*n^9 + (2226946937/1034643456000)*n^8 - (263782703/2715939072000)*n^7 + (3455599541/129330432000)*n^6 - (31330211789/754427520000)*n^5 + (2559599737/7185024000)*n^4 - (3245092381/7334712000)*n^3 + (7079701/6350400)*n^2 - (28181/27720)*n + 1

%e Some solutions for n=5

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 23 2011