%I #3 Dec 12 2018 12:34:20
%S 1,1,9,35,199,1005,5475,29469,161685,889759,4932641,27453471,
%T 153432241,860203135,4836370101,27257082723,153943314903,871064225325,
%U 4936953721755,28022734759125,159272314734843,906343638290133,5163219745287591,29442990216677985,168050775902585751,959985125666243145,5488145767630988595,31397773111113948245,179747041781229841375
%N a(n) = [x^n*y^n] 1/(1 - x - y - x^2 + x*y - y^2).
%C Central terms of triangle A123603.
%e Triangle A123603 of coefficients of x^(n-k)*y^k in 1/(1 - x - y - x^2 + x*y - y^2), for n >= 0 and k = 0..n, begins
%e 1;
%e 1, 1;
%e 2, 1, 2;
%e 3, 3, 3, 3;
%e 5, 5, 9, 5, 5;
%e 8, 10, 17, 17, 10, 8;
%e 13, 18, 36, 35, 36, 18, 13;
%e 21, 33, 69, 81, 81, 69, 33, 21;
%e 34, 59, 133, 167, 199, 167, 133, 59, 34;
%e 55, 105, 249, 345, 435, 435, 345, 249, 105, 55;
%e 89, 185, 462, 687, 945, 1005, 945, 687, 462, 185, 89; ...
%e in which the central terms form this sequence.
%o (PARI) {a(n) = polcoeff( polcoeff( 1/(1 - x - y - x^2 + x*y - y^2 +x*O(x^n) +y*O(y^n)),n,x),n,y)}
%o for(n=0,30, print1(a(n),", "))
%Y Cf. A123603, A192364.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 12 2018