%I #5 Sep 13 2013 17:16:43

%S 1,2,2,6,8,6,20,36,30,20,70,160,168,112,70,252,700,900,720,420,252,

%T 924,3024,4620,4400,2970,1584,924,3432,12936,22932,25480,20020,12012,

%U 6006,3432,12870,54912,110880,141120,127400,87360,48048,22880,12870,48620

%N Triangle T(n,k) = binomial(2*n,k) *binomial(2*n-2*k,n-k), read by rows; 0<=k<=n.

%C Row sums are s(n) = 1, 4, 20, 106, 580, 3244,,...

%F Conjecture for row sums: 2*(n+1)*(2*n+1)*s(n) +(-81*n^2+19*n-8)*s(n-1) +10*(51*n^2-77*n+30)*s(n-2) -500*(n-1)*(2*n-3)*s(n-3)=0. - _R. J. Mathar_, Sep 13 2013

%e 1;

%e 2, 2;

%e 6, 8, 6;

%e 20, 36, 30, 20;

%e 70, 160, 168, 112, 70;

%e 252, 700, 900, 720, 420, 252;

%e 924, 3024, 4620, 4400, 2970, 1584, 924;

%e 3432, 12936, 22932, 25480, 20020, 12012, 6006, 3432;

%e 12870, 54912, 110880, 141120, 127400, 87360, 48048, 22880, 12870;

%e 48620, 231660, 525096, 753984, 771120, 599760, 371280, 190944, 87516, 48620';

%e 184756, 972400, 2445300, 3912480, 4476780, 3907008, 2713200, 1550400, 755820, 335920, 184756;

%t t[n_, m_] = (Binomial[2*n, m]*Binomial[2*(n - m), (n - m)]); Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

%Y Cf. A062344.

%K nonn,tabl

%O 0,2

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 17 2008