%I #11 Jun 06 2024 08:23:13
%S 1,1,1,1,3,3,1,1,6,15,20,12,6,1,1,10,45,120,190,192,140,80,30,10,1,1,
%T 15,105,455,1290,2382,3385,3195,2880,1860,1098,435,240,60,15,1,1,21,
%U 210,1330,5775,17157,36092,60210,75075,87185,68775,64470,38395,26355,13125,7987,2394,1365,560,105,21,1,1,28,378,3276,19985,86772,265286,595136,1104642,1499680,2036412,2057496,2115855,1729672,1508580,912128,755300,378336,260848,120120,80388,26384,16856,4200,3640,840,168,28,1
%N Triangle read by rows: T(n,k), n >=1, 0 <= k <= C(n,k), = number of n X n symmetric positive definite matrices with 2's on the main diagonal and 1's and 0's elsewhere and with k 1's above the diagonal.
%H <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%e 1;
%e 1,1;
%e 1,3,3,1;
%e 1,6,15,20,12,6,1;
%e ...
%Y Rows sums give A085657.
%Y A085656(n) = Sum_{k=0..C(n,2)} 2^k * T(n,k).
%K nonn,tabf
%O 1,5
%A _N. J. A. Sloane_, Jul 13 2003
%E Rows n=6..8 added by _Max Alekseyev_, Jun 04 2024