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begins:\n  0: 1;\n  1: 0,     1;\n  2: 0,     1,      1;\n  3: 0,     2,      3,      1;\n  4: 0,     6,     11,      6,     1;\n  5: 0,    24,     50,     35,    10,     1;\n  6: 0,   120,    274,    225,    85,    15,    1;\n  7: 0,   720,   1764,   1624,   735,   175,   21,   1;\n  8: 0,  5040,  13068,  13132,  6769,  1960,  322,  28,  1;\n  9: 0, 40320, 109584, 118124, 67284, 22449, 4536, 546, 36, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (n-1+x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(n - 1 + x)*P[n - 1, x]];\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 - 1 + x)*v[i - 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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1764,    1624,    735,    175,    21,    1;\n  7:   5040,   13068,   13132,   6769,   1960,   322,   28,   1;\n  8:  40320,  109584,  118124,  67284,  22449,  4536,  546,  36,  1;\n  9: 362880, 1026576, 1172700, 723680, 269325, 63273, 9450, 870, 45, 1;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in ascending powers of x, starting at the lowest nonzero coefficient, where P(n,x) = (n+x)*P(n-1,x) for n >= 1, with P(0,x) = x.","mathematica":"P[0, x_] := x;\nP[n_, x_] := P[n, x] = Expand[(n + x)*P[n - 1, x]];\nTable[PadRight[CoefficientList[Expand[P[n, x]/x^Exponent[P[n, x], x, Min]], x], n + 1], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = x; for(n = 1, N, my(i = n + 1); v[i] = (n + x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p/x^valuation(p, x))); c = concat(c, vector(n + 1 - #c)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, 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