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begins:\n  0:         1;\n  1:         9,         12,           4;\n  2:        81,        216,         216,          96,           16;\n  3:       729,       2916,        4860,        4320,         2160,          576,           64;\n  4:      6561,      34992,       81648,      108864,        90720,        48384,        16128,         3072,          256;\n  5:     59049,     393660,     1180980,     2099520,      2449440,      1959552,      1088640,       414720,       103680,        15360,         1024;\n  6:    531441,    4251528,    15588936,    34642080,     51963120,     55427328,     43110144,     24634368,     10264320,      3041280,       608256,        73728,        4096;\n  7:   4782969,   44641044,   193444524,   515852064,    945728784,   1260971712,   1260971712,    960740352,    560431872,    249080832,     83026944,     20127744,     3354624,      344064,      16384;\n  8:  43046721,  459165024,  2295825120,  7142567040,  15475561920,  24760899072,  30263321088,  28822210560,  21616657920,  12809871360,   5977939968,   2173796352,   603832320,   123863040,   17694720,   1572864,    65536;\n  9: 387420489, 4649045868, 26344593252, 93669664896, 234174162240, 437125102848, 631402926336, 721603344384, 661469732352, 489977579520, 293986547712, 142538932224, 55431806976, 17055940608, 4060938240, 721944576, 90243072, 7077888, 262144;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (9+12*x+4*x^2)*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 + 12*x + 4*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] = 1; for(n = 1, N, my(i = n + 1); v[i] = (9 + 12*x + 4*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}}],"derivation":{"root":"n-cdb0db4ad473ee28","steps":["basis A013609","x \u21a6 x+1"],"edges":["e-20c0b01c4fb345ed","e-606ea858cc2070d2"],"text":"basis-map coefficients of A297191, shifted \u2192 basis A013609 \u2192 x \u21a6 x+1"},"headline":"basis-map coefficients of A297191, shifted \u2192 basis A013609 \u2192 x \u21a6 x+1","chain":null}