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begins:\n  0:  0;\n  1:  3;\n  2:  6,  18;\n  3:  9,  54,   81;\n  4: 12, 108,  324,   324;\n  5: 15, 180,  810,  1620,   1215;\n  6: 18, 270, 1620,  4860,   7290,   4374;\n  7: 21, 378, 2835, 11340,  25515,  30618,  15309;\n  8: 24, 504, 4536, 22680,  68040, 122472, 122472,  52488;\n  9: 27, 648, 6804, 40824, 153090, 367416, 551124, 472392, 177147;\n","recurrence_sentence":"The row polynomials satisfy (n-1)*P(n,x) = (n+3*n*x)*P(n-1,x) for n >= 2, with P(0,x) = 0, P(1,x) = 3.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 3;\nP[n_, x_] := P[n, x] = Expand[Together[((n + 3*n*x)*P[n - 1, x])/(n - 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 0; v[2] = 3; for(n = 2, N, my(i = n + 1); v[i] = ((n + 3*n*x)*v[i - 1])/(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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