The linear recurrence operator annihilating the series of coefficients of th\
    e Onsager series is



      3                                3       2
     n  (4 n + 9)       2 (n + 1) (16 n  + 71 n  + 95 n + 35) N
- ------------------- + ---------------------------------------
                    3                               3
  (4 n + 15) (n + 6)              (4 n + 15) (n + 6)

                    3        2                 2
       (n + 2) (52 n  + 367 n  + 952 n + 888) N
     - -----------------------------------------
                                    3
                  (4 n + 15) (n + 6)

                     2               3
       4 (n + 3) (9 n  + 54 n + 76) N
     + -------------------------------
                               3
             (4 n + 15) (n + 6)

                    3        2                   4
       (n + 4) (52 n  + 569 n  + 2164 n + 2844) N
     + -------------------------------------------
                                     3
                   (4 n + 15) (n + 6)

                      3        2                  5
       2 (n + 5) (16 n  + 217 n  + 971 n + 1435) N     6
     - -------------------------------------------- + N
                                     3
                   (4 n + 15) (n + 6)



                             and in Maple notation



-n^3*(4*n+9)/(4*n+15)/(n+6)^3+2*(n+1)*(16*n^3+71*n^2+95*n+35)/(4*n+15)/(n+6)^3*
N-(n+2)*(52*n^3+367*n^2+952*n+888)/(4*n+15)/(n+6)^3*N^2+4*(n+3)*(9*n^2+54*n+76)
/(4*n+15)/(n+6)^3*N^3+(n+4)*(52*n^3+569*n^2+2164*n+2844)/(4*n+15)/(n+6)^3*N^4-2
*(n+5)*(16*n^3+217*n^2+971*n+1435)/(4*n+15)/(n+6)^3*N^5+N^6