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begins:\n   1:   1;\n   2:   2,       1;\n   3:   4,       8,        1;\n   4:   8,      52,       20,         1;\n   5:  16,     320,      292,        40,         1;\n   6:  32,    1936,     3824,      1092,        70,        1;\n   7:  64,   11648,    47824,     25664,      3192,      112,       1;\n   8: 128,   69952,   585536,    561104,    121424,     7896,     168,     1;\n   9: 256,  419840,  7096384,  11807616,   4203824,   453056,   17304,   240,   1;\n  10: 512, 2519296, 85576448, 243248704, 137922336, 23232176, 1422080, 34584, 330, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (2+x)*P(n-1,x) + 4*x*d/dx P(n-1,x) + x^2*d^2/dx^2 P(n-1,x) for n >= 2, with P(1,x) = 1.","mathematica":"P[1, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(2 + x)*P[n - 1, x] + 4*x*D[P[n - 1, x], x] + x^2*D[P[n - 1, x], {x, 2}]];\nTable[CoefficientList[P[n, x], x], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1; for(n = 2, N, my(i = n); v[i] = (2 + x)*v[i - 1] + 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