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begins:\n  0:   1;\n  1:   2,     8;\n  2:   4,    32,     64;\n  3:   8,    96,    384,     512;\n  4:  16,   256,   1536,    4096,     4096;\n  5:  32,   640,   5120,   20480,    40960,    32768;\n  6:  64,  1536,  15360,   81920,   245760,   393216,    262144;\n  7: 128,  3584,  43008,  286720,  1146880,  2752512,   3670016,   2097152;\n  8: 256,  8192, 114688,  917504,  4587520, 14680064,  29360128,  33554432,  16777216;\n  9: 512, 18432, 294912, 2752512, 16515072, 66060288, 176160768, 301989888, 301989888, 134217728;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (2+8*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 + 8*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 + 8*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":"A038214","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:   2,     8;\n  2:   4,    32,     64;\n  3:   8,    96,    384,     512;\n  4:  16,   256,   1536,    4096,     4096;\n  5:  32,   640,   5120,   20480,    40960,    32768;\n  6:  64,  1536,  15360,   81920,   245760,   393216,    262144;\n  7: 128,  3584,  43008,  286720,  1146880,  2752512,   3670016,   2097152;\n  8: 256,  8192, 114688,  917504,  4587520, 14680064,  29360128,  33554432,  16777216;\n  9: 512, 18432, 294912, 2752512, 16515072, 66060288, 176160768, 301989888, 301989888, 134217728;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (2+8*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 + 8*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] = (2 + 8*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}},{"oeis_id":"A038280","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:         8,         2;\n  2:        64,        32,         4;\n  3:       512,       384,        96,         8;\n  4:      4096,      4096,      1536,       256,       16;\n  5:     32768,     40960,     20480,      5120,      640,       32;\n  6:    262144,    393216,    245760,     81920,    15360,     1536,      64;\n  7:   2097152,   3670016,   2752512,   1146880,   286720,    43008,    3584,    128;\n  8:  16777216,  33554432,  29360128,  14680064,  4587520,   917504,  114688,   8192,   256;\n  9: 134217728, 301989888, 301989888, 176160768, 66060288, 16515072, 2752512, 294912, 18432, 512;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (2+8*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 + 8*x)*P[n - 1, x]];\nTable[Reverse[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] = (2 + 8*x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); c = Vecrev(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":true,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-ae7910bbe46f8a41","steps":["basis A013611"],"edges":["e-d7d2422771947afc"],"text":"A130123 \u2192 basis A013611"},"headline":"A130123 \u2192 basis A013611","chain":null}