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30,   35,    14;\n  5: 1, 15,  70,  140,   126,    42;\n  6: 1, 21, 140,  420,   630,   462,   132;\n  7: 1, 28, 252, 1050,  2310,  2772,  1716,   429;\n  8: 1, 36, 420, 2310,  6930, 12012, 12012,  6435,  1430;\n  9: 1, 45, 660, 4620, 18018, 42042, 60060, 51480, 24310, 4862;\n","recurrence_sentence":"The row polynomials satisfy (n+1)*P(n,x) = (2*n-1+(4*n-2)*x)*P(n-1,x) - (n-2)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 1 + x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1 + x;\nP[n_, x_] := P[n, x] = Expand[Together[((2*n - 1 + (4*n - 2)*x)*P[n - 1, x] - (n - 2)*P[n - 2, x])/(n + 1)]];\nTable[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] = 1 + x; for(n = 2, N, my(i = n + 1); v[i] = ((2*n - 1 + (4*n - 2)*x)*v[i - 1] - (n - 2)*v[i - 2])/(n + 1)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, 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