%I #4 Dec 01 2013 06:02:07

%S 7,14,14,25,45,25,41,130,130,41,61,336,650,336,61,86,755,2942,2942,

%T 755,86,117,1494,11445,24520,11445,1494,117,156,2696,37040,178630,

%U 178630,37040,2696,156,204,4713,101369,1054179,2547039,1054179,101369,4713,204

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays x(i,j) with row sums sum{j^3*x(i,j), j=1..k+1} nondecreasing, and column sums sum{i^3*x(i,j), i=1..n+1} nondecreasing

%C Table starts

%C ...7....14......25........41..........61...........86..........117..........156

%C ..14....45.....130.......336.........755.........1494.........2696.........4713

%C ..25...130.....650......2942.......11445........37040.......101369.......257799

%C ..41...336....2942.....24520......178630......1054179......4995346.....20815986

%C ..61...755...11445....178630.....2547039.....29338491....266176765...2040969695

%C ..86..1494...37040...1054179....29338491....672737568..12123627839.180942639975

%C .117..2696..101369...4995346...266176765..12123627839.449539533113

%C .156..4713..257799..20815986..2040969695.180942639975

%C .204..8039..633068..81415483.14195455926

%C .262.13380.1515898.310059665

%H R. H. Hardin, <a href="/A232860/b232860.txt">Table of n, a(n) for n = 1..97</a>

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 01 2013