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12;\n  4:    420,     560,     210,      20;\n  5:   1980,    3600,    2160,     480,      30;\n  6:   9009,   20790,   17325,    6300,     945,     42;\n  7:  40040,  112112,  120120,   61600,   15400,   1680,    56;\n  8: 175032,  576576,  756756,  504504,  180180,  33264,  2772,   72;\n  9: 755820, 2864160, 4455360, 3669120, 1719900, 458640, 65520, 4320, 90;\n","recurrence_sentence":"The row polynomials satisfy (4*n^4+2*n^3-10*n^2+4*n)*P(n,x) = -((48*n^4-48*n^3-12*n^2+12*n)*x^2-(4*n^4-4*n^3-10*n^2+10*n)*x^3)*P(n-3,x) - ((16*n^4-16*n^3-4*n^2+4*n)*x^3+(3*n^2-3*n)*x^4)*d/dx P(n-3,x) - (64*n^4-32*n^3-16*n^2+8*n-(16*n^4-8*n^3-16*n^2+8*n)*x+(12*n^4-6*n^3-12*n^2+6*n)*x^2)*P(n-2,x) + ((64*n^4-32*n^3-16*n^2+8*n)*x+(32*n^4-16*n^3+4*n^2-2*n)*x^2+(6*n^2-3*n)*x^3)*d/dx P(n-2,x) + (32*n^4-40*n^2+8+(12*n^4-12*n^2)*x)*P(n-1,x) - ((16*n^4-20*n^2+4)*x+(3*n^2-3)*x^2)*d/dx P(n-1,x) for n >= 3, with P(0,x) = 0, P(1,x) = 2, P(2,x) = 15 + 6*x.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 2;\nP[2, x_] := 15 + 6*x;\nP[n_, x_] := P[n, x] = Expand[Together[(-((48*n^4 - 48*n^3 - 12*n^2 + 12*n)*x^2 - (4*n^4 - 4*n^3 - 10*n^2 + 10*n)*x^3)*P[n - 3, x] - ((16*n^4 - 16*n^3 - 4*n^2 + 4*n)*x^3 + (3*n^2 - 3*n)*x^4)*D[P[n - 3, x], x] - (64*n^4 - 32*n^3 - 16*n^2 + 8*n - (16*n^4 - 8*n^3 - 16*n^2 + 8*n)*x + (12*n^4 - 6*n^3 - 12*n^2 + 6*n)*x^2)*P[n - 2, x] + ((64*n^4 - 32*n^3 - 16*n^2 + 8*n)*x + (32*n^4 - 16*n^3 + 4*n^2 - 2*n)*x^2 + (6*n^2 - 3*n)*x^3)*D[P[n - 2, x], x] + (32*n^4 - 40*n^2 + 8 + (12*n^4 - 12*n^2)*x)*P[n - 1, x] - ((16*n^4 - 20*n^2 + 4)*x + (3*n^2 - 3)*x^2)*D[P[n - 1, x], x])/(4*n^4 + 2*n^3 - 10*n^2 + 4*n)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 0; v[2] = 2; v[3] = 15 + 6*x; for(n = 3, N, my(i = n + 1); v[i] = (-((48*n^4 - 48*n^3 - 12*n^2 + 12*n)*x^2 - (4*n^4 - 4*n^3 - 10*n^2 + 10*n)*x^3)*v[i - 3] - ((16*n^4 - 16*n^3 - 4*n^2 + 4*n)*x^3 + (3*n^2 - 3*n)*x^4)*deriv(v[i - 3], x) - (64*n^4 - 32*n^3 - 16*n^2 + 8*n - (16*n^4 - 8*n^3 - 16*n^2 + 8*n)*x + (12*n^4 - 6*n^3 - 12*n^2 + 6*n)*x^2)*v[i - 2] + ((64*n^4 - 32*n^3 - 16*n^2 + 8*n)*x + (32*n^4 - 16*n^3 + 4*n^2 - 2*n)*x^2 + (6*n^2 - 3*n)*x^3)*deriv(v[i - 2], x) + (32*n^4 - 40*n^2 + 8 + (12*n^4 - 12*n^2)*x)*v[i - 1] - ((16*n^4 - 20*n^2 + 4)*x + (3*n^2 - 3)*x^2)*deriv(v[i - 1], x))/(4*n^4 + 2*n^3 - 10*n^2 + 4*n)); 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-984320118b653f6b","steps":["basis A007318","D"],"edges":["e-2345ffa617ccabd7","e-abb34fcab799982f"],"text":"A132812 \u2192 basis A007318 \u2192 D"},"headline":"A132812 \u2192 basis A007318 \u2192 D","chain":null}