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real-rooted with all roots in (-inf, 0]"}]}],"used_by":[],"used_by_total":0,"links":[],"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: 1;\n 1: 41, 52, 16;\n 2: 1681, 4264, 4016, 1664, 256;\n 3: 68921, 262236, 413280, 345280, 161280, 39936, 4096;\n 4: 2825761, 14335568, 31683488, 39842816, 31179520, 15548416, 4825088, 851968, 65536;\n 5: 115856201, 734697860, 2089684720, 3510465920, 3857122560, 2896305152, 1505218560, 534609920, 124190720, 17039360, 1048576;\n 6: 4750104241, 36147134712, 125735061456, 264347873920, 374121208320, 375486339072, 274035789824, 146531254272, 56975032320, 15710289920, 2916089856, 327155712, 16777216;\n 7: 194754273881, 1729037943724, 7110790192576, 17954840181824, 31096819968256, 39078808717312, 36746696347648, 26265423921152, 14340174184448, 5951323635712, 1848095277056, 416414695424, 64357400576, 6106906624, 268435456;\n 8: 7984925229121, 81017777934496, 384568439351360, 1133574144568320, 2322393951234560, 3506543238668288, 4036261723045888, 3612971530321920, 2541696327024640, 1409940109393920, 614683522367488, 208395135090688, 53861742018560, 10259603128320, 1358283407360, 111669149696, 4294967296;\n 9: 327381934393961, 3736945007228628, 20107989269665488, 67770383220523776, 160317102547791360, 282669944562690048, 384985282275385344, 414122134160277504, 356664256553484288, 247783297975582720, 139186051337945088, 63066785452130304, 22879814805356544, 6555776474677248, 1450976854671360, 239362822373376, 27715423961088, 2010044694528, 68719476736;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (41+52*x+16*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[(41 + 52*x + 16*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] = (41 + 52*x + 16*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-b30e7a5b4198051a","steps":["basis A013611","x \u21a6 x+1"],"edges":["e-a99971f11d0aad5a","e-8d91781e67228b49"],"text":"A272866 \u2192 basis A013611 \u2192 x \u21a6 x+1"},"headline":"A272866 \u2192 basis A013611 \u2192 x \u21a6 x+1","chain":null}