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160;\n  4:  240,    9528,     57984,      76224,       19200,         384;\n  5:  494,   34344,    374856,     999616,      686880,       94848,         896;\n  6: 1004,  116864,   2117616,    9996160,    14117440,     5609472,      449792,        2048;\n  7: 2026,  382720,  10924608,   83862656,   209656640,   174793728,    42864640,     2074624,       4608;\n  8: 4072, 1221096,  52883712,  623239296,  2515879680,  3739435776,  1974325248,   312600576,    9381888,    10240;\n  9: 8166, 3826168, 244504440, 4244382336, 26001965760, 62404717824, 59421352704, 20864378880, 2203872768, 41809920, 22528;\n","recurrence_sentence":"The row polynomials satisfy (n+1)*P(n,x) = -(2*n+4+(4*n^2+8*n)*x+(4*n^3+12*n^2+8*n)*x^2)*P(n-2,x) - ((n+2)*x+(2*n^2+4*n)*x^2-(4*n^2+12*n+8)*x^3)*d/dx P(n-2,x) + (3*n+4+(4*n^2+8*n+4)*x)*P(n-1,x) + ((n+1)*x-(2*n+2)*x^2)*d/dx P(n-1,x) for n >= 2, with P(0,x) = 8 + 8*x, P(1,x) = 22 + 88*x + 24*x^2.","mathematica":"P[0, x_] := 8 + 8*x;\nP[1, x_] := 22 + 88*x + 24*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[(-(2*n + 4 + (4*n^2 + 8*n)*x + (4*n^3 + 12*n^2 + 8*n)*x^2)*P[n - 2, x] - ((n + 2)*x + (2*n^2 + 4*n)*x^2 - (4*n^2 + 12*n + 8)*x^3)*D[P[n - 2, x], x] + (3*n + 4 + (4*n^2 + 8*n + 4)*x)*P[n - 1, x] + ((n + 1)*x - (2*n + 2)*x^2)*D[P[n - 1, x], x])/(n + 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 8 + 8*x; v[2] = 22 + 88*x + 24*x^2; for(n = 2, N, my(i = n + 1); v[i] = (-(2*n + 4 + (4*n^2 + 8*n)*x + (4*n^3 + 12*n^2 + 8*n)*x^2)*v[i - 2] - ((n + 2)*x + (2*n^2 + 4*n)*x^2 - (4*n^2 + 12*n + 8)*x^3)*deriv(v[i - 2], x) + (3*n + 4 + (4*n^2 + 8*n + 4)*x)*v[i - 1] + ((n + 1)*x - (2*n + 2)*x^2)*deriv(v[i - 1], x))/(n + 1)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, 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