Logarithm of Bar-Natan's rational associator 1/48*[AB] -1/1440*[A[A[AB]]] +1/1152*[A[B[AB]]] +1/60480*[A[A[A[A[AB]]]]] +1/1451520*[A[A[A[B[AB]]]]] +13/1161216*[A[A[B[B[AB]]]]] +17/1451520*[A[B[A[A[AB]]]]] +1/1451520*[A[B[A[B[AB]]]]] -1/48*[BA] +1/1440*[B[B[BA]]] -1/1152*[B[A[BA]]] -1/60480*[B[B[B[B[BA]]]]] -1/1451520*[B[B[B[A[BA]]]]] -13/1161216*[B[B[A[A[BA]]]]] -17/1451520*[B[A[B[B[BA]]]]] -1/1451520*[B[A[B[A[BA]]]]] Expansion of the monomials present in BN's ratonal associator over the (filtered) Hall basis: [A[B[AB]]] - AABB + 2*ABAB - 2*BABA + BBAA; [0,0,-1,0,2,0,0,0,0,-2,0,1,0,0]; ==> C22 (B,(B,(B,A))) - ABBB + 3*BABB - 3*BBAB + BBBA; [0,0,0,0,0,0,-1,0,0,0,3,0,-3,1]; ==> -C31 (B,(A,(B,A))) AABB - 2*ABAB + 2*BABA - BBAA; [0,0,1,0,-2,0,0,0,0,2,0,-1,0,0]; ==> -C22 (A,(A,(A,(A,(A,B))))) = c15 (A,(A,(A,(B,(A,B))))) = c24 + 2*c11c13 (A,(A,(B,(B,(A,B))))) = c33 + 3*c11c22 (A,(B,(A,(A,(A,B))))) = c24 + c11c13 (A,(B,(A,(B,(A,B))))) = c33 + 2*c11c22 - c12c21 (B,(B,(B,(B,(B,A))))) = - c51 (B,(B,(B,(A,(B,A))))) = - c42 (B,(B,(A,(A,(B,A))))) = - c33 (B,(A,(B,(B,(B,A))))) = - c42 - c11c31 (B,(A,(B,(A,(B,A))))) = - c33 - c11c22 + c12c21