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Examples

			L.g.f.: L(x,y) = (x + y)/1 + (3*x^2 + 2*x*y + 3*y^2)/2 + (4*x^3 + 3*x^2*y + 3*x*y^2 + 4*y^3)/3 + (7*x^4 + 4*x^3*y + 10*x^2*y^2 + 4*x*y^3 + 7*y^4)/4 + (6*x^5 + 5*x^4*y + 10*x^3*y^2 + 10*x^2*y^3 + 5*x*y^4 + 6*y^5)/5 + (12*x^6 + 6*x^5*y + 21*x^4*y^2 + 26*x^3*y^3 + 21*x^2*y^4 + 6*x*y^5 + 12*y^6)/6 + (8*x^7 + 7*x^6*y + 21*x^5*y^2 + 35*x^4*y^3 + 35*x^3*y^4 + 21*x^2*y^5 + 7*x*y^6 + 8*y^7)/7 + (15*x^8 + 8*x^7*y + 36*x^6*y^2 + 56*x^5*y^3 + 90*x^4*y^4 + 56*x^3*y^5 + 36*x^2*y^6 + 8*x*y^7 + 15*y^8)/8 + ...
such that
exp( L(x,y) ) = Product_{n>=1} 1/(1 - (x^n + y^n)), or
L(x,y) = Sum_{n>=1} -log(1 - (x^n + y^n)),
where
L(x,y) = Sum_{n>=0} Sum_{k>=0} T(n,k) * x^n*y^k/(n+k),
in which the constant term is taken to be zero: L(0,0) = 0.
SQUARE TABLE.
The square table of coefficients T(n,k) of x^n*y^k/(n+k) in L(x,y) begins
0, 1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, ...;
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, ...;
3, 3, 10, 10, 21, 21, 36, 36, 55, 55, 78, 78, 105, ...;
4, 4, 10, 26, 35, 56, 93, 120, 165, 232, 286, 364, ...;
7, 5, 21, 35, 90, 126, 230, 330, 537, 715, 1043, 1365, ...;
6, 6, 21, 56, 126, 262, 462, 792, 1287, 2002, 3018, ...;
12, 7, 36, 93, 230, 462, 994, 1716, 3073, 5035, 8120, ...;
8, 8, 36, 120, 330, 792, 1716, 3446, 6435, 11440, 19448, ...;
15, 9, 55, 165, 537, 1287, 3073, 6435, 13050, 24310, 44010, ...;
13, 10, 55, 232, 715, 2002, 5035, 11440, 24310, 48698, 92378, ...;
18, 11, 78, 286, 1043, 3018, 8120, 19448, 44010, 92378, 185310, ...;
12, 12, 78, 364, 1365, 4368, 12376, 31824, 75582, 167960, 352716, ...; ...
TRIANGLE.
Alternatively, this sequence may be written as a triangle, starting as
0;
1, 1;
3, 2, 3;
4, 3, 3, 4;
7, 4, 10, 4, 7;
6, 5, 10, 10, 5, 6;
12, 6, 21, 26, 21, 6, 12;
8, 7, 21, 35, 35, 21, 7, 8;
15, 8, 36, 56, 90, 56, 36, 8, 15;
13, 9, 36, 93, 126, 126, 93, 36, 9, 13;
18, 10, 55, 120, 230, 262, 230, 120, 55, 10, 18;
12, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 12;
28, 12, 78, 232, 537, 792, 994, 792, 537, 232, 78, 12, 28;
14, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 14;
24, 14, 105, 364, 1043, 2002, 3073, 3446, 3073, 2002, 1043, 364, 105, 14, 24;
24, 15, 105, 470, 1365, 3018, 5035, 6435, 6435, 5035, 3018, 1365, 470, 105, 15, 24;
31, 16, 136, 560, 1892, 4368, 8120, 11440, 13050, 11440, 8120, 4368, 1892, 560, 136, 16, 31; ...
where L(x,y) = Sum_{n>=0} Sum_{k=0..n} T(n-k,k)*x^(n-k)*y^k / n.