%I #9 Feb 28 2013 09:03:46

%S 128,1375,10238,62347,331561,1595475,7102354,29688844,117789230,

%T 447095308,1633583432,5773429726,19814156786,66246078602,216345953850,

%U 691705334522,2169266885114,6684119486458,20264694041594,60526805714938,178299235266554,518528519151610,1490041038438394,4234162281971706,11906594366685178

%N Number of Bottleneck-Monge matrices with 7 rows.

%C Bottleneck-Monge matrices are {0,1} matrices A in which, for every i<j and k<l, max(A[i,l],A[j,k]) <= max(A[i,k],A[j,l]).

%H Nathaniel Johnston, <a href="/A070055/b070055.txt">Table of n, a(n) for n = 1..400</a>

%F a(N) = a(7, N), where a(P, N) is defined recursively in A070050.

%F Empirical G.f.: -x*(8192*x^13 -101240*x^12 +472850*x^11 -1238864*x^10 +2119510*x^9 -2555238*x^8 +2264076*x^7 -1508235*x^6 +762058*x^5 -290820*x^4 +82129*x^3 -16377*x^2 +2081*x -128) / ((x -1)*(2*x -1)^13). - _Colin Barker_, Feb 28 2013

%Y Cf. A070050, A070051, A070052, A070053, A070054, A070056, A070057.

%K nonn

%O 1,1

%A Pascal Prea (pascal.prea(AT)lim.univ-mrs.fr), Apr 18 2002

%E a(10) - a(25) from _Nathaniel Johnston_, Apr 13 2011