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begins:\n  0:    0;\n  1:    2;\n  2:    8,     8;\n  3:   24,    48,     24;\n  4:   64,   192,    192,     64;\n  5:  160,   640,    960,    640,    160;\n  6:  384,  1920,   3840,   3840,   1920,    384;\n  7:  896,  5376,  13440,  17920,  13440,   5376,    896;\n  8: 2048, 14336,  43008,  71680,  71680,  43008,  14336,  2048;\n  9: 4608, 36864, 129024, 258048, 322560, 258048, 129024, 36864, 4608;\n","recurrence_sentence":"The row polynomials satisfy (n-1)*P(n,x) = (2*n+2*n*x)*P(n-1,x) for n >= 2, with P(0,x) = 0, P(1,x) = 2.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 2;\nP[n_, x_] := P[n, x] = Expand[Together[((2*n + 2*n*x)*P[n - 1, x])/(n - 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 0; v[2] = 2; for(n = 2, N, my(i = n + 1); v[i] = ((2*n + 2*n*x)*v[i - 1])/(n - 1)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-d28ad9841fc73317","steps":["D"],"edges":["e-a49f8ff31c907f66"],"text":"A038208 \u2192 D"},"headline":"A038208 \u2192 D","chain":null}