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begins:\n  0:         1;\n  1:         9,          3;\n  2:        81,         54,          9;\n  3:       729,        729,        243,         27;\n  4:      6561,       8748,       4374,        972,        81;\n  5:     59049,      98415,      65610,      21870,      3645,       243;\n  6:    531441,    1062882,     885735,     393660,     98415,     13122,      729;\n  7:   4782969,   11160261,   11160261,    6200145,   2066715,    413343,    45927,    2187;\n  8:  43046721,  114791256,  133923132,   89282088,  37200870,   9920232,  1653372,  157464,   6561;\n  9: 387420489, 1162261467, 1549681956, 1205308188, 602654094, 200884698, 44641044, 6377292, 531441, 19683;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (9+3*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[(9 + 3*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] = (9 + 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 - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}},{"oeis_id":"A038227","target":"reversed_triangle","first_row":0,"oeis_offset":0,"reversed":true,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:     1;\n  1:     3,      9;\n  2:     9,     54,      81;\n  3:    27,    243,     729,      729;\n  4:    81,    972,    4374,     8748,      6561;\n  5:   243,   3645,   21870,    65610,     98415,     59049;\n  6:   729,  13122,   98415,   393660,    885735,   1062882,     531441;\n  7:  2187,  45927,  413343,  2066715,   6200145,  11160261,   11160261,    4782969;\n  8:  6561, 157464, 1653372,  9920232,  37200870,  89282088,  133923132,  114791256,   43046721;\n  9: 19683, 531441, 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v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":true,"trim_zeros":"none","regular_triangle":true}},{"oeis_id":"A038293","target":"triangle","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:         1;\n  1:         9,          3;\n  2:        81,         54,          9;\n  3:       729,        729,        243,         27;\n  4:      6561,       8748,       4374,        972,        81;\n  5:     59049,      98415,      65610,      21870,      3645,       243;\n  6:    531441,    1062882,     885735,     393660,     98415,     13122,      729;\n  7:   4782969,   11160261,   11160261,    6200145,   2066715,    413343,    45927,    2187;\n  8:  43046721,  114791256,  133923132,   89282088,  37200870,   9920232,  1653372,  157464,   6561;\n  9: 387420489, 1162261467, 1549681956, 1205308188, 602654094, 200884698, 44641044, 6377292, 531441, 19683;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (9+3*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[(9 + 3*x)*P[n - 1, x]];\nTable[PadRight[CoefficientList[P[n, x], x], n + 1], {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] = (9 + 3*x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); 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":true}}],"derivation":{"root":"n-366b2525683554ec","steps":["basis A013610"],"edges":["e-b4f43a8046f9cfa3"],"text":"A038279 \u2192 basis A013610"},"headline":"A038279 \u2192 basis A013610","chain":null}