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begins:\n   1: 1,  6,   9;\n   2: 1,  9,  27,   27;\n   3: 1, 12,  54,  108,    81;\n   4: 1, 15,  90,  270,   405,    243;\n   5: 1, 18, 135,  540,  1215,   1458,    729;\n   6: 1, 21, 189,  945,  2835,   5103,   5103,   2187;\n   7: 1, 24, 252, 1512,  5670,  13608,  20412,  17496,    6561;\n   8: 1, 27, 324, 2268, 10206,  30618,  61236,  78732,   59049,   19683;\n   9: 1, 30, 405, 3240, 17010,  61236, 153090, 262440,  295245,  196830,  59049;\n  10: 1, 33, 495, 4455, 26730, 112266, 336798, 721710, 1082565, 1082565, 649539, 177147;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (1+3*x)*P(n-1,x) for n >= 2, with P(1,x) = 1 + 6*x + 9*x^2.","mathematica":"P[1, x_] := 1 + 6*x + 9*x^2;\nP[n_, x_] := P[n, x] = Expand[(1 + 3*x)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1 + 6*x + 9*x^2; for(n = 2, N, my(i = n); v[i] = (1 + 3*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, v[i])))};\nT(10)","reading":{"first_row":1,"offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-5fe240122e98ffb3","steps":["basis A013610"],"edges":["e-33def10999a9e794"],"text":"basis-map coefficients of A112227 \u2192 basis A013610"},"headline":"basis-map coefficients of A112227 \u2192 basis A013610","chain":null}