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20312500,    114453125,    120109375,     41658750,      5998125,      400050,      12810,       188,       1;\n  7:   201562500,   1657421875,   2327578125,   1064453125,    204225000,    18676875,     866250,     20550,     234,     1;\n  8:  2007812500,  24264453125,  45293359375,  26807343750,   6659640625,   800848125,   50386875,   1716000,   31350,   285,   1;\n  9: 20039062500, 357982421875, 885598828125, 669930078125, 211175937500, 32445737500, 2656355625, 121666875, 3168000, 45925, 341, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = -(50-15*x-4*x^2)*P(n-2,x) - (25*x-20*x^2)*d/dx P(n-2,x) + (15-3*x)*P(n-1,x) + 5*x*d/dx P(n-1,x) for n >= 2, with P(0,x) = 40 + 17*x + x^2, P(1,x) = 300 + 235*x + 33*x^2 + x^3.","mathematica":"P[0, x_] := 40 + 17*x + x^2;\nP[1, x_] := 300 + 235*x + 33*x^2 + x^3;\nP[n_, x_] := P[n, x] = Expand[-(50 - 15*x - 4*x^2)*P[n - 2, x] - (25*x - 20*x^2)*D[P[n - 2, x], x] + (15 - 3*x)*P[n - 1, x] + 5*x*D[P[n - 1, x], x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 40 + 17*x + x^2; v[2] = 300 + 235*x + 33*x^2 + x^3; for(n = 2, N, my(i = n + 1); v[i] = -(50 - 15*x - 4*x^2)*v[i - 2] - (25*x - 20*x^2)*deriv(v[i - 2], x) + (15 - 3*x)*v[i - 1] + 5*x*deriv(v[i - 1], x)); v};\nrow(n, p) = {my(c = Vecrev(p)); 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":false}}],"derivation":{"root":"n-77f76afdd288bbc1","steps":["D+1"],"edges":["e-30a379ded1234e92"],"text":"A075500 \u2192 D+1"},"headline":"A075500 \u2192 D+1","chain":null}