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1,   8,    9;\n  3: -1, -12,  -27,   -16;\n  4:  1,  16,   54,    64,    25;\n  5: -1, -20,  -90,  -160,  -125,   -36;\n  6:  1,  24,  135,   320,   375,   216,    49;\n  7: -1, -28, -189,  -560,  -875,  -756,  -343,   -64;\n  8:  1,  32,  252,   896,  1750,  2016,  1372,   512,   81;\n  9: -1, -36, -324, -1344, -3150, -4536, -4116, -2304, -729, -100;\n","recurrence_sentence":"The row polynomials satisfy (1+(3*n-1)*x+n^2*x^2)*P(n,x) = -(1+(3*n+3)*x+(n^2+5*n+3)*x^2+(n^2+2*n+1)*x^3)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[(-(1 + (3*n + 3)*x + (n^2 + 5*n + 3)*x^2 + (n^2 + 2*n + 1)*x^3)*P[n - 1, x])/(1 + (3*n - 1)*x + n^2*x^2)]];\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] = (-(1 + (3*n + 3)*x + (n^2 + 5*n + 3)*x^2 + (n^2 + 2*n + 1)*x^3)*v[i - 1])/(1 + (3*n - 1)*x + n^2*x^2)); 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-74c1e94669ff21ff","steps":["(\u03b8+1)\u00b2"],"edges":["e-0045543824a8afca"],"text":"basis-map coefficients of A113214, shifted \u2192 (\u03b8+1)\u00b2"},"headline":"basis-map coefficients of A113214, shifted \u2192 (\u03b8+1)\u00b2","chain":null}