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begins:\n  0: 1;\n  1: 1, 1;\n  2: 0, 2, 1;\n  3: 0, 1, 3, 1;\n  4: 0, 0, 3, 4,  1;\n  5: 0, 0, 1, 6,  5,  1;\n  6: 0, 0, 0, 4, 10,  6,  1;\n  7: 0, 0, 0, 1, 10, 15,  7,  1;\n  8: 0, 0, 0, 0,  5, 20, 21,  8, 1;\n  9: 0, 0, 0, 0,  1, 15, 35, 28, 9, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = x*P(n-1,x) + x*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[x*P[n - 1, x] + 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 + x; for(n = 2, N, my(i = n + 1); v[i] = x*v[i - 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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