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begins:\n  0:      1;\n  1:      4,      12;\n  2:     16,      96,      144;\n  3:     64,     576,     1728,      1728;\n  4:    256,    3072,    13824,     27648,      20736;\n  5:   1024,   15360,    92160,    276480,     414720,     248832;\n  6:   4096,   73728,   552960,   2211840,    4976640,    5971968,     2985984;\n  7:  16384,  344064,  3096576,  15482880,   46448640,   83607552,    83607552,    35831808;\n  8:  65536, 1572864, 16515072,  99090432,  371589120,  891813888,  1337720832,  1146617856,   429981696;\n  9: 262144, 7077888, 84934656, 594542592, 2675441664, 8026324992, 16052649984, 20639121408, 15479341056, 5159780352;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (4+12*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[(4 + 12*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] = (4 + 12*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":"A038242","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:      4,      12;\n  2:     16,      96,      144;\n  3:     64,     576,     1728,      1728;\n  4:    256,    3072,    13824,     27648,      20736;\n  5:   1024,   15360,    92160,    276480,     414720,     248832;\n  6:   4096,   73728,   552960,   2211840,    4976640,    5971968,     2985984;\n  7:  16384,  344064,  3096576,  15482880,   46448640,   83607552,    83607552,    35831808;\n  8:  65536, 1572864, 16515072,  99090432,  371589120,  891813888,  1337720832,  1146617856,   429981696;\n  9: 262144, 7077888, 84934656, 594542592, 2675441664, 8026324992, 16052649984, 20639121408, 15479341056, 5159780352;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (4+12*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[(4 + 12*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] = (4 + 12*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":"A038330","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:         12,           4;\n  2:        144,          96,          16;\n  3:       1728,        1728,         576,          64;\n  4:      20736,       27648,       13824,        3072,        256;\n  5:     248832,      414720,      276480,       92160,      15360,       1024;\n  6:    2985984,     5971968,     4976640,     2211840,     552960,      73728,      4096;\n  7:   35831808,    83607552,    83607552,    46448640,   15482880,    3096576,    344064,    16384;\n  8:  429981696,  1146617856,  1337720832,   891813888,  371589120,   99090432,  16515072,  1572864,   65536;\n  9: 5159780352, 15479341056, 20639121408, 16052649984, 8026324992, 2675441664, 594542592, 84934656, 7077888, 262144;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (4+12*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[(4 + 12*x)*P[n - 1, 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