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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:          89,           228,           144;\n  1:         881,          3336,          4176,           1728;\n  2:        8721,         43704,         81648,          67392,          20736;\n  3:       86329,        538356,       1336752,        1651968,        1016064,          248832;\n  4:      854569,       6375804,      19746144,       32493312,       29963520,        14681088,         2985984;\n  5:     8459361,      73474512,     272634336,      560234880,      688538880,       506124288,       206032896,        35831808;\n  6:    83739041,     829881648,    3588291360,     8841467520,    13578243840,     13309028352,      8130834432,      2830712832,      429981696;\n  7:   828931049,    9230210460,   45568859040,   130913936640,   241191509760,    295523085312,    240810651648,    125841309696,    38268370944,     5159780352;\n  8:  8205571449,  101419395540,  562862824560,  1847124207360,  3969304093440,   5836219941888,   5946252705792,   4145310203904,  1892349444096,   510818254848,   61917364224;\n  9: 81226783441, 1103430602328, 6800092133040, 25094682031680, 61617339912960, 105698325454848, 129256355708928, 112682293198848, 68628948516864, 27811216097280, 6748992700416, 743008370688;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = -P(n-2,x) + (10+12*x)*P(n-1,x) for n >= 2, with P(0,x) = 89 + 228*x + 144*x^2, P(1,x) = 881 + 3336*x + 4176*x^2 + 1728*x^3.","mathematica":"P[0, x_] := 89 + 228*x + 144*x^2;\nP[1, x_] := 881 + 3336*x + 4176*x^2 + 1728*x^3;\nP[n_, x_] := P[n, x] = Expand[-P[n - 2, x] + (10 + 12*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] = 89 + 228*x + 144*x^2; v[2] = 881 + 3336*x + 4176*x^2 + 1728*x^3; for(n = 2, N, my(i = n + 1); v[i] = -v[i - 2] + (10 + 12*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-8eb9bb3a09f0b7fd","steps":["basis A013610","basis A013609"],"edges":["e-8cd26e1d1ff01e6d","e-57243e9dfbc1d8ef"],"text":"A123519 \u2192 basis A013610 \u2192 basis A013609"},"headline":"A123519 \u2192 basis A013610 \u2192 basis A013609","chain":null}