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612360000,      529079040,      180033840;\n  7:    5160960,    216760320,    2194698240,    9754214400,    22861440000,    29628426240,    20163790080,     5643509760;\n  8:   92897280,   4459069440,   52672757760,  280921374720,   823011840000,  1422164459520,  1451792885760,   812665405440,   192849310080;\n  9: 1857945600, 100329062400, 1354442342400, 8427641241600, 29628426240000, 63997400678400, 87107573145600, 73139886489600, 34712875814400, 7142567040000;\n","recurrence_sentence":"The row polynomials satisfy (4+(18*n-6)*x+9*n^2*x^2)*P(n,x) = (8*n+8+(36*n^2+72*n+36)*x+(18*n^3+108*n^2+144*n+54)*x^2+(27*n^3+81*n^2+81*n+27)*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[((8*n + 8 + (36*n^2 + 72*n + 36)*x + (18*n^3 + 108*n^2 + 144*n + 54)*x^2 + (27*n^3 + 81*n^2 + 81*n + 27)*x^3)*P[n - 1, x])/(4 + (18*n - 6)*x + 9*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] = ((8*n + 8 + (36*n^2 + 72*n + 36)*x + (18*n^3 + 108*n^2 + 144*n + 54)*x^2 + (27*n^3 + 81*n^2 + 81*n + 27)*x^3)*v[i - 1])/(4 + (18*n - 6)*x + 9*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-75a6475b3e851dc5","steps":["basis A013610","(\u03b8+1)\u00b2"],"edges":["e-1eb90284df2d6b2d","e-3eac6e908782d88e"],"text":"A156992 \u2192 basis A013610 \u2192 (\u03b8+1)\u00b2"},"headline":"A156992 \u2192 basis A013610 \u2192 (\u03b8+1)\u00b2","chain":null}