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begins:\n  0:    1;\n  1:   -2,    -2;\n  2:    4,     8,      4;\n  3:   -8,   -24,    -24,     -8;\n  4:   16,    64,     96,     64,     16;\n  5:  -32,  -160,   -320,   -320,   -160,    -32;\n  6:   64,   384,    960,   1280,    960,    384,     64;\n  7: -128,  -896,  -2688,  -4480,  -4480,  -2688,   -896,   -128;\n  8:  256,  2048,   7168,  14336,  17920,  14336,   7168,   2048,   256;\n  9: -512, -4608, -18432, -43008, -64512, -64512, -43008, -18432, -4608, -512;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = -(2+2*x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[-(2 + 2*x)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = -(2 + 2*x)*v[i - 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-74c1e94669ff21ff","steps":["basis A013609"],"edges":["e-b6cdc8ab0f2a09ef"],"text":"basis-map coefficients of A113214, shifted \u2192 basis A013609"},"headline":"basis-map coefficients of A113214, shifted \u2192 basis A013609","chain":null}