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begins:\n  0:      1;\n  1:      1,       1;\n  2:      2,       3,       1;\n  3:      6,      11,       6,      1;\n  4:     24,      50,      35,     10,      1;\n  5:    120,     274,     225,     85,     15,     1;\n  6:    720,    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":"The row polynomials satisfy P(n,x) = (n+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 + 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 + 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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 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":"The row polynomials satisfy P(n,x) = (n+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 + x)*P[n - 1, x]];\nTable[PadRight[CoefficientList[P[n, x], x], n + 1], {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 + x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-efe23a76953cf69d","steps":[],"edges":[],"text":"A130534"},"headline":"A130534: Triangle T(n,k), 0 <= k <= n, read by rows, giving coefficients of the polynomial (x+1)(x+2)...(x+n), expanded 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