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satisfy (n+2+(3*n+6)*x+(3*n+6)*x^2+(n+2)*x^3)*P(n,x) = (n+2+(2*n+22)*x-(14*n-86)*x^2-(60*n-162)*x^3-(91*n-160)*x^4-(62*n-80)*x^5-(16*n-16)*x^6)*P(n-1,x) + (2*x+16*x^2+52*x^3+88*x^4+82*x^5+40*x^6+8*x^7)*d/dx P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[((n + 2 + (2*n + 22)*x - (14*n - 86)*x^2 - (60*n - 162)*x^3 - (91*n - 160)*x^4 - (62*n - 80)*x^5 - (16*n - 16)*x^6)*P[n - 1, x] + (2*x + 16*x^2 + 52*x^3 + 88*x^4 + 82*x^5 + 40*x^6 + 8*x^7)*D[P[n - 1, x], x])/(n + 2 + (3*n + 6)*x + (3*n + 6)*x^2 + (n + 2)*x^3)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = ((n + 2 + (2*n + 22)*x - (14*n - 86)*x^2 - (60*n - 162)*x^3 - (91*n - 160)*x^4 - (62*n - 80)*x^5 - (16*n - 16)*x^6)*v[i - 1] + (2*x + 16*x^2 + 52*x^3 + 88*x^4 + 82*x^5 + 40*x^6 + 8*x^7)*deriv(v[i - 1], x))/(n + 2 + (3*n + 6)*x + (3*n + 6)*x^2 + (n + 2)*x^3)); v};\nrow(n, p) = 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