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167,     1258,      1044,        170,          1;\n  5:    678,    11641,     21928,       8190,        682,          1;\n  6:   2725,    97074,    376095,     298340,      60795,       2730,         1;\n  7:  10916,   758533,   5502834,    8548375,    3578720,     439299,     10922,        1;\n  8:  43683,  5691778,  72057130,  200883894,  159840020,   40021982,   3129822,    43690,      1;\n  9: 174754, 41633433, 874030896, 4072886868, 5682679524, 2653716366, 429539232, 22127364, 174762, 1;\n","recurrence_sentence":"The row polynomials satisfy (3*n-8+6*x)*P(n,x) = -(12*n-20+(18*n^2-87*n+119)*x+(27*n^3-189*n^2+450*n-404)*x^2+(81*n^2-378*n+423)*x^3+(54*n-90)*x^4)*P(n-2,x) - ((9*n-15)*x+(27*n^2-126*n+153)*x^2-(27*n^2-198*n+327)*x^3-(81*n-243)*x^4-54*x^5)*d/dx P(n-2,x) + (15*n-37+(18*n^2-87*n+134)*x+(45*n-111)*x^2+18*x^3)*P(n-1,x) + ((9*n-24)*x-(9*n-42)*x^2-18*x^3)*d/dx P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 2 + x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 2 + x;\nP[n_, x_] := P[n, x] = Expand[Together[(-(12*n - 20 + (18*n^2 - 87*n + 119)*x + (27*n^3 - 189*n^2 + 450*n - 404)*x^2 + (81*n^2 - 378*n + 423)*x^3 + (54*n - 90)*x^4)*P[n - 2, x] - ((9*n - 15)*x + (27*n^2 - 126*n + 153)*x^2 - (27*n^2 - 198*n + 327)*x^3 - (81*n - 243)*x^4 - 54*x^5)*D[P[n - 2, x], x] + (15*n - 37 + (18*n^2 - 87*n + 134)*x + (45*n - 111)*x^2 + 18*x^3)*P[n - 1, x] + ((9*n - 24)*x - (9*n - 42)*x^2 - 18*x^3)*D[P[n - 1, x], x])/(3*n - 8 + 6*x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 2 + x; for(n = 2, N, my(i = n + 1); v[i] = (-(12*n - 20 + (18*n^2 - 87*n + 119)*x + (27*n^3 - 189*n^2 + 450*n - 404)*x^2 + (81*n^2 - 378*n + 423)*x^3 + (54*n - 90)*x^4)*v[i - 2] - ((9*n - 15)*x + (27*n^2 - 126*n + 153)*x^2 - (27*n^2 - 198*n + 327)*x^3 - (81*n - 243)*x^4 - 54*x^5)*deriv(v[i - 2], x) + (15*n - 37 + (18*n^2 - 87*n + 134)*x + (45*n - 111)*x^2 + 18*x^3)*v[i - 1] + ((9*n - 24)*x - (9*n - 42)*x^2 - 18*x^3)*deriv(v[i - 1], 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