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  190,      90,       10;\n  4:   240,     975,     825,      210,      15;\n  5:   672,    4431,    5985,     2625,     420,      21;\n  6:  1792,   18620,   37828,    25480,    6860,     756,     28;\n  7:  4608,   74124,  218484,   212436,   85680,   15624,   1260,    36;\n  8: 11520,  283725, 1185075,  1600830,  908145,  243810,  32130,  1980,   45;\n  9: 28160, 1054405, 6140475, 11231275, 8616300, 3195885, 612150, 61050, 2970, 55;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (8+19*x+9*x^2+x^3)*P(n-3,x) + (19*x+18*x^2+3*x^3)*d/dx P(n-3,x) + (9*x^2+3*x^3)*d^2/dx^2 P(n-3,x) + x^3*d^3/dx^3 P(n-3,x) - (12+15*x+3*x^2)*P(n-2,x) - (15*x+6*x^2)*d/dx P(n-2,x) - 3*x^2*d^2/dx^2 P(n-2,x) + (6+3*x)*P(n-1,x) + 3*x*d/dx P(n-1,x) for n >= 3, with P(0,x) = 1, P(1,x) = 6 + 3*x, P(2,x) = 24 + 30*x + 6*x^2.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 6 + 3*x;\nP[2, x_] := 24 + 30*x + 6*x^2;\nP[n_, x_] := P[n, x] = Expand[(8 + 19*x + 9*x^2 + x^3)*P[n - 3, x] + (19*x + 18*x^2 + 3*x^3)*D[P[n - 3, x], x] + (9*x^2 + 3*x^3)*D[P[n - 3, x], {x, 2}] + x^3*D[P[n - 3, x], {x, 3}] - (12 + 15*x + 3*x^2)*P[n - 2, x] - (15*x + 6*x^2)*D[P[n - 2, x], x] - 3*x^2*D[P[n - 2, x], {x, 2}] + (6 + 3*x)*P[n - 1, x] + 3*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] = 1; v[2] = 6 + 3*x; v[3] = 24 + 30*x + 6*x^2; for(n = 3, N, my(i = n + 1); v[i] = (8 + 19*x + 9*x^2 + x^3)*v[i - 3] + (19*x + 18*x^2 + 3*x^3)*deriv(v[i - 3], x) + (9*x^2 + 3*x^3)*deriv(deriv(v[i - 3], x), x) + x^3*deriv(deriv(deriv(v[i - 3], x), x), x) - (12 + 15*x + 3*x^2)*v[i - 2] - (15*x + 6*x^2)*deriv(v[i - 2], x) - 3*x^2*deriv(deriv(v[i - 2], x), x) + (6 + 3*x)*v[i - 1] + 3*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-7f1b09730105c8f0","steps":["basis A008277"],"edges":["e-79b34479614e907f"],"text":"A094305 \u2192 basis A008277"},"headline":"A094305 \u2192 basis A008277","chain":null}