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A013609","chain":null}},{"id":"l-be5bb2b01f95a571","kind":"fingerprint_related","node_a_id":"n-6a4f4798749d2440","node_b_id":"n-01f9460eada72015","fingerprint":"f6-8d10fbbacee008e8","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-8d10fbbacee008e8"},"other_id":"n-6a4f4798749d2440","other":{"id":"n-6a4f4798749d2440","name":"basis_map_A013609 of Triangle whose (i,j)-th entry is binomial(i,j)*6^(i-j).","first_index":0,"fingerprint":"f6-8d10fbbacee008e8","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["7","2"],["49","28","4"]],"card_rows":[["1"],["7","2"],["49","28","4"],["343","294","84","8"]],"row_sums_preview":["1","9","81","729","6561","59049","531441","4782969"],"regions":["(-inf, 0]","(-inf, -1]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-22693abd431a71f2","steps":["basis A013609"],"edges":["e-4c464713c83c5f6b"],"text":"A038255 \u2192 basis A013609"},"headline":"A038255 \u2192 basis A013609","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:              784,               448,                64;\n  1:            21952,             18816,              5376,               512;\n  2:           614656,            702464,            301056,             57344,              4096;\n  3:         17210368,          24586240,          14049280,           4014080,            573440,            32768;\n  4:        481890304,         826097664,         590069760,         224788480,          48168960,          5505024,           262144;\n  5:      13492928512,       26985857024,       23130734592,       11014635520,        3147038720,        539492352,         51380224,         2097152;\n  6:     377801998336,      863547424768,      863547424768,      493455671296,      176234168320,      40282095616,       5754585088,       469762048,       16777216;\n  7:   10578455953408,    27201743880192,    31087707291648,    20725138194432,     8882202083328,    2537772023808,     483385147392,     59190018048,     4227858432,     134217728;\n  8:  296196766695424,   846276476272640,  1088069755207680,   829005527777280,   414502763888640,  142115233333248,   33836960317440,   5524401684480,   591900180480,   37580963840,   1073741824;\n  9: 8293509467471872, 26065315469197312, 37236164955996160, 31916712819425280, 18238121611100160, 7295248644440064, 2084356755554304, 425378929704960, 60768418529280, 5787468431360, 330712481792, 8589934592;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (28+8*x)*P(n-1,x) for n >= 1, with P(0,x) = 784 + 448*x + 64*x^2.","mathematica":"P[0, x_] := 784 + 448*x + 64*x^2;\nP[n_, x_] := P[n, x] = Expand[(28 + 8*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] = 784 + 448*x + 64*x^2; for(n = 1, N, my(i = n + 1); v[i] = (28 + 8*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-6874f381e9c7e0a2","steps":["x \u21a6 x+1","x \u21a6 x+1"],"edges":["e-4a3b4bf6a80699a3","e-b097c5c47d554a10"],"text":"A038334 \u2192 x \u21a6 x+1 \u2192 x \u21a6 x+1"},"headline":"A038334 \u2192 x \u21a6 x+1 \u2192 x \u21a6 x+1","chain":null}