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21;\n  2:        81,        378,         441;\n  3:       729,       5103,       11907,         9261;\n  4:      6561,      61236,      214326,       333396,        194481;\n  5:     59049,     688905,     3214890,      7501410,       8751645,       4084101;\n  6:    531441,    7440174,    43401015,    135025380,     236294415,     220541454,      85766121;\n  7:   4782969,   78121827,   546852789,   2126649735,    4962182715,    6947055801,    5403265623,    1801088541;\n  8:  43046721,  803538792,  6562233468,  30623756184,   89319288870,  166729339224,  194517562428,  129678374952,   37822859361;\n  9: 387420489, 8135830269, 75934415844, 413420708484, 1446972479694, 3376269119286, 5251974185556, 5251974185556, 3063651608241, 794280046581;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (9+21*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 + 21*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 + 21*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}}],"derivation":{"root":"n-f485cd65a8f8089f","steps":["x \u21a6 x+1","reverse"],"edges":["e-62ade03cd9f25f04","e-4b512ae2958817e5"],"text":"A038335 \u2192 x \u21a6 x+1 \u2192 reverse"},"headline":"A038335 \u2192 x \u21a6 x+1 \u2192 reverse","chain":null}