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1200,   2000,     800,      80;\n  6: 114,  3534,  10260,    7410,    1710,    114;\n  7: 154,  9702,  46354,   53900,   21560,   3234,    154;\n  8: 200, 25400, 193200,  340200,  210000,  53200,   5600,  200;\n  9: 252, 64260, 762300, 1958040, 1751652, 666792, 116424, 9072, 252;\n","recurrence_sentence":"The row polynomials satisfy (9*n^2-21*n+10)*P(n,x) = -(9*n^2-3*n-2+(27*n^2-9*n-6)*x+(9*n^2-3*n-2)*x^2)*P(n-2,x) - ((27*n^2-9*n-6)*x+(18*n^2-6*n-4)*x^2)*d/dx P(n-2,x) - (9*n^2-3*n-2)*x^2*d^2/dx^2 P(n-2,x) + (18*n^2-24*n-10+(18*n^2-24*n-10)*x)*P(n-1,x) + (18*n^2-24*n-10)*x*d/dx P(n-1,x) for n >= 2, with P(0,x) = 0, P(1,x) = 4.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 4;\nP[n_, x_] := P[n, x] = Expand[Together[(-(9*n^2 - 3*n - 2 + (27*n^2 - 9*n - 6)*x + (9*n^2 - 3*n - 2)*x^2)*P[n - 2, x] - ((27*n^2 - 9*n - 6)*x + (18*n^2 - 6*n - 4)*x^2)*D[P[n - 2, x], x] - (9*n^2 - 3*n - 2)*x^2*D[P[n - 2, x], {x, 2}] + (18*n^2 - 24*n - 10 + (18*n^2 - 24*n - 10)*x)*P[n - 1, x] + (18*n^2 - 24*n - 10)*x*D[P[n - 1, x], x])/(9*n^2 - 21*n + 10)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 0; v[2] = 4; for(n = 2, N, my(i = n + 1); v[i] = (-(9*n^2 - 3*n - 2 + (27*n^2 - 9*n - 6)*x + (9*n^2 - 3*n - 2)*x^2)*v[i - 2] - ((27*n^2 - 9*n - 6)*x + (18*n^2 - 6*n - 4)*x^2)*deriv(v[i - 2], x) - (9*n^2 - 3*n - 2)*x^2*deriv(deriv(v[i - 2], x), x) + (18*n^2 - 24*n - 10 + (18*n^2 - 24*n - 10)*x)*v[i - 1] + (18*n^2 - 24*n - 10)*x*deriv(v[i - 1], x))/(9*n^2 - 21*n + 10)); 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-ccc86c3dcf2ac685","steps":["D","basis A008277"],"edges":["e-7e9b074076a3cdbe","e-6493b71a6558fb19"],"text":"A131431 \u2192 D \u2192 basis A008277"},"headline":"A131431 \u2192 D \u2192 basis A008277","chain":null}