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A013610","D"],"edges":["e-b9cdb58d54bdc029","e-108da488069017c7"],"text":"A038255 \u2192 basis A013610 \u2192 D"},"headline":"A038255 \u2192 basis A013610 \u2192 D","chain":null}}],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","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:        36,        168,          196;\n  1:       216,       1512,         3528,         2744;\n  2:      1296,      12096,        42336,        65856,         38416;\n  3:      7776,      90720,       423360,       987840,       1152480,         537824;\n  4:     46656,     653184,      3810240,     11854080,      20744640,       19361664,        7529536;\n  5:    279936,    4572288,     32006016,    124467840,     290424960,      406594944,      316240512,      105413504;\n  6:   1679616,   31352832,    256048128,   1194891264,    3485099520,     6505519104,     7589772288,     5059848192,     1475789056;\n  7:  10077696,  211631616,   1975228416,  10754021376,   37639074816,    87824507904,   136615901184,   136615901184,    79692609024,    20661046784;\n  8:  60466176, 1410877440,  14814213120,  92177326080,  376390748160,  1053894094848,  2049238517760,  2732318023680,  2390778270720,  1239662807040,   289254654976;\n  9: 362797056, 9311791104, 108637562880, 760462940160, 3548827054080, 11592835043328, 27049948434432, 45083247390720, 52597121955840, 40908872632320, 19090807228416, 4049565169664;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (6+14*x)*P(n-1,x) for n >= 1, with P(0,x) = 36 + 168*x + 196*x^2.","mathematica":"P[0, x_] := 36 + 168*x + 196*x^2;\nP[n_, x_] := P[n, x] = Expand[(6 + 14*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] = 36 + 168*x + 196*x^2; for(n = 1, N, my(i = n + 1); v[i] = (6 + 14*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-c11cb6bca0e3e7dc","steps":["basis A007318","reverse"],"edges":["e-37fb8ca4839f71ce","e-57e373e08b265a38"],"text":"A038284 \u2192 basis A007318 \u2192 reverse"},"headline":"A038284 \u2192 basis A007318 \u2192 reverse","chain":null}