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begins:\n  0: 1;\n  1: 1,  1;\n  2: 1,  4,   1;\n  3: 1,  7,   7,    1;\n  4: 1, 10,  22,   10,    1;\n  5: 1, 13,  46,   46,   13,    1;\n  6: 1, 16,  79,  136,   79,   16,    1;\n  7: 1, 19, 121,  307,  307,  121,   19,   1;\n  8: 1, 22, 172,  586,  886,  586,  172,  22,  1;\n  9: 1, 25, 232, 1000, 2086, 2086, 1000, 232, 25, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (1+x)*P(n-1,x) + 2*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[(1 + x)*P[n - 1, x] + 2*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] = (1 + x)*v[i - 1] + 2*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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