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begins:\n  0:  1;\n  1:  1;\n  2:  2,   1;\n  3:  3,   2;\n  4:  5,   5,   1;\n  5:  8,  10,   3;\n  6: 13,  20,   9,  1;\n  7: 21,  38,  22,  4;\n  8: 34,  71,  51, 14, 1;\n  9: 55, 130, 111, 40, 5;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = P(n-1,x) + (1+x)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 1.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[P[n - 1, x] + (1 + x)*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; for(n = 2, N, my(i = n + 1); v[i] = v[i - 1] + (1 + x)*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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