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begins:\n  0: 1;\n  1: 1,  2;\n  2: 1,  4,   3;\n  3: 1,  6,   9,   4;\n  4: 1,  8,  18,  16,   5;\n  5: 1, 10,  30,  40,  25,   6;\n  6: 1, 12,  45,  80,  75,  36,   7;\n  7: 1, 14,  63, 140, 175, 126,  49,   8;\n  8: 1, 16,  84, 224, 350, 336, 196,  64,  9;\n  9: 1, 18, 108, 336, 630, 756, 588, 288, 81, 10;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (2+2*x)*P(n-1,x) - (1+2*x+x^2)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 1 + 2*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1 + 2*x;\nP[n_, x_] := P[n, x] = Expand[(2 + 2*x)*P[n - 1, x] - (1 + 2*x + x^2)*P[n - 2, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 1 + 2*x; for(n = 2, N, my(i = n + 1); v[i] = (2 + 2*x)*v[i - 1] - (1 + 2*x + x^2)*v[i - 2]); 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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