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begins:\n  0: 0,     1;\n  1: 0,     3,      4,       1;\n  2: 0,     9,     24,      22,       8,        1;\n  3: 0,    27,    108,     171,     136,       57,       12,        1;\n  4: 0,    81,    432,     972,    1200,      886,      400,      108,       16,        1;\n  5: 0,   243,   1620,    4725,    7920,     8430,     5944,     2810,      880,      175,       20,       1;\n  6: 0,   729,   5832,   20898,   44280,    61695,    59472,    40636,    19824,     6855,     1640,     258,      24,      1;\n  7: 0,  2187,  20412,   86751,  222264,   383103,   469476,   421491,   281488,   140497,    52164,   14189,    2744,    357,     28,     1;\n  8: 0,  6561,  69984,  344088, 1034208,  2125116,  3163104,  3525480,  2999904,  1968934,   999968,  391720,  117152,  26236,   4256,   472,   32,   1;\n  9: 0, 19683, 236196, 1318761, 4548960, 10856268, 19023984, 25353972, 26264736, 21431898, 13875544, 7143966, 2918304, 939036, 234864, 44676, 6240, 603, 36, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (3+4*x+x^2)*P(n-1,x) for n >= 1, with P(0,x) = x.","mathematica":"P[0, x_] := x;\nP[n_, x_] := P[n, x] = Expand[(3 + 4*x + x^2)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = x; for(n = 1, N, my(i = n + 1); v[i] = (3 + 4*x + x^2)*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":"A299989","target":"triangle","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0: 0,     1;\n  1: 0,     3,      4,       1;\n  2: 0,     9,     24,      22,       8,        1;\n  3: 0,    27,    108,     171,     136,       57,       12,        1;\n  4: 0,    81,    432,     972,    1200,      886,      400,      108,       16,        1;\n  5: 0,   243,   1620,    4725,    7920,     8430,     5944,     2810,      880,      175,       20,       1;\n  6: 0,   729,   5832,   20898,   44280,    61695,    59472,    40636,    19824,     6855,     1640,     258,      24,      1;\n  7: 0,  2187,  20412,   86751,  222264,   383103,   469476,   421491,   281488,   140497,    52164,   14189,    2744,    357,     28,     1;\n  8: 0,  6561,  69984,  344088, 1034208,  2125116,  3163104,  3525480,  2999904,  1968934,   999968,  391720,  117152,  26236,   4256,   472,   32,   1;\n  9: 0, 19683, 236196, 1318761, 4548960, 10856268, 19023984, 25353972, 26264736, 21431898, 13875544, 7143966, 2918304, 939036, 234864, 44676, 6240, 603, 36, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (3+4*x+x^2)*P(n-1,x) for n >= 1, with P(0,x) = x.","mathematica":"P[0, x_] := x;\nP[n_, x_] := P[n, x] = Expand[(3 + 4*x + x^2)*P[n - 1, 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