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50;\n  3:   16,   120,    300,     250;\n  4:   32,   320,   1200,    2000,    1250;\n  5:   64,   800,   4000,   10000,   12500,     6250;\n  6:  128,  1920,  12000,   40000,   75000,    75000,    31250;\n  7:  256,  4480,  33600,  140000,  350000,   525000,   437500,   156250;\n  8:  512, 10240,  89600,  448000, 1400000,  2800000,  3500000,  2500000,   781250;\n  9: 1024, 23040, 230400, 1344000, 5040000, 12600000, 21000000, 22500000, 14062500, 3906250;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (2+7*x+5*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 2.","mathematica":"P[0, x_] := 2;\nP[n_, x_] := P[n, x] = Expand[Together[((2 + 7*x + 5*x^2)*P[n - 1, x])/(1 + x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 2; for(n = 1, N, my(i = n + 1); v[i] = ((2 + 7*x + 5*x^2)*v[i - 1])/(1 + x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, 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