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252,    6300,    25200,     25200,      6300,       252;\n  6:   924,   33264,   207900,    369600,    207900,     33264,       924;\n  7:  3432,  168168,  1513512,   4204200,   4204200,   1513512,    168168,     3432;\n  8: 12870,  823680, 10090080,  40360320,  63063000,  40360320,  10090080,   823680,   12870;\n  9: 48620, 3938220, 63011520, 343062720, 771891120, 771891120, 343062720, 63011520, 3938220, 48620;\n","recurrence_sentence":"The row polynomials satisfy n^2*P(n,x) = (8*n^2-8*n+2+(8*n^2-8*n+2)*x)*P(n-1,x) - (16*n^2-32*n+12-(32*n^2-64*n+24)*x+(16*n^2-32*n+12)*x^2)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 2 + 2*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 2 + 2*x;\nP[n_, x_] := P[n, x] = Expand[Together[((8*n^2 - 8*n + 2 + (8*n^2 - 8*n + 2)*x)*P[n - 1, x] - (16*n^2 - 32*n + 12 - (32*n^2 - 64*n + 24)*x + (16*n^2 - 32*n + 12)*x^2)*P[n - 2, x])/(n^2)]];\nTable[PadRight[CoefficientList[P[n, x], x], n + 1], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] 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924;\n  7:  3432,  168168,  1513512,   4204200,   4204200,   1513512,    168168,     3432;\n  8: 12870,  823680, 10090080,  40360320,  63063000,  40360320,  10090080,   823680,   12870;\n  9: 48620, 3938220, 63011520, 343062720, 771891120, 771891120, 343062720, 63011520, 3938220, 48620;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where n^2*P(n,x) = (8*n^2-8*n+2+(8*n^2-8*n+2)*x)*P(n-1,x) - (16*n^2-32*n+12-(32*n^2-64*n+24)*x+(16*n^2-32*n+12)*x^2)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 2 + 2*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 2 + 2*x;\nP[n_, x_] := P[n, x] = Expand[Together[((8*n^2 - 8*n + 2 + (8*n^2 - 8*n + 2)*x)*P[n - 1, x] - (16*n^2 - 32*n + 12 - (32*n^2 - 64*n + 24)*x + (16*n^2 - 32*n + 12)*x^2)*P[n - 2, x])/(n^2)]];\nTable[Reverse[PadRight[CoefficientList[P[n, x], x], n + 1]], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 2 + 2*x; for(n = 2, N, my(i = n + 1); v[i] = ((8*n^2 - 8*n + 2 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