A086623 Symmetric square table of coefficients, read by antidiagonals, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = (1-xy)/[(1-x)(1-y)] + xy*f(x,y)^2.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 4, 8, 8, 4, 1, 1, 5, 14, 19, 14, 5, 1, 1, 6, 22, 40, 40, 22, 6, 1, 1, 7, 32, 76, 100, 76, 32, 7, 1, 1, 8, 44, 132, 222, 222, 132, 44, 8, 1, 1, 9, 58, 213, 448, 570, 448, 213, 58, 9, 1, 1, 10, 74, 324, 834, 1316, 1316, 834, 324, 74, 10, 1, 1

Offset: 0

Author

Paul D. Hanna, Jul 24 2003

Keywords

• nonn
• tabl

Comments

The first row and column of 1's together form: (1-xy)/[(1-x)(1-y)], while the remaining square table (excluding the first row and column) give the coefficients of f(x,y)^2.

Examples

			Rows begin:
1,1,_1,__1,___1,___1,____1,____1,_____1, ...
1,1,_2,__3,___4,___5,____6,____7,_____8, ...
1,2,_4,__8,__14,__22,___32,___44,____58, ...
1,3,_8,_19,__40,__76,__132,__213,___324, ...
1,4,14,_40,_100,_222,__448,__834,__1450, ...
1,5,22,_76,_222,_570,_1316,_2782,__5458, ...
1,6,32,132,_448,1316,_3442,_8180,_17928, ...
1,7,44,213,-834,2782,_8180,21685,_52694, ...
1,8,58,324,1450,5458,17928,52694,141112, ...
		

Crossrefs

Cf. A086624 (diagonal), A086625 (antidiagonal sums).