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real_rooted","from_index":0,"region_key":"(-inf, 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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:         1;\n  1:        27,         57,           18;\n  2:       288,       1566,         2925,          2052,           324;\n  3:      2484,      22032,        78489,        141453,        131706,          55404,            5832;\n  4:     19440,     239760,      1267488,       3729564,       6619401,        7140312,         4426488,         1329696,          104976;\n  5:    143856,    2274480,     15969960,      65396160,     172288215,      303367761,       358237890,       275649480,       128070720,         29918160,          1889568;\n  6:   1026432,   19805472,    173525328,     911483280,    3190570560,     7819412922,     13704801237,     17207849628,     15220863900,       9101419200,       3381381936,        646232256,         34012224;\n  7:   7138368,  162642816,   1708484400,   10957079952,   47875468284,   150536948688,    350581136661,    612644517765,    804148978122,     784404317844,     554577342984,     271159621488,      83925162720,      13570877376,       612220032;\n  8:  48708864, 1279867392,  15677535744,  118766487168,  622342447776,  2389698648288,   6947669018304,  15577633391544,  27168173753553,   36879126013296,   38684387787696,   30847397894208,   18162714683232,    7511123499264,   1992163984128,    279172334592,    11019960576;\n  9: 327525120, 9750170880, 136457042688, 1192483689984, 7288247064096, 33063299956512, 115296183526608, 315714478512384, 687409598738835, 1197202755113001, 1668482106359922, 1851259273447248, 1616916470097600, 1090276788692448, 549970417476288, 197047915059456, 45721816429824, 5653239775488, 198359290368;\n","recurrence_sentence":"The row polynomials satisfy (7*n-5+(12*n-5)*x+6*x^2)*P(n,x) = (42*n+12+(219*n+84)*x+(378*n+219)*x^2+(216*n+252)*x^3+108*x^4)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[((42*n + 12 + (219*n + 84)*x + (378*n + 219)*x^2 + (216*n + 252)*x^3 + 108*x^4)*P[n - 1, x])/(7*n - 5 + (12*n - 5)*x + 6*x^2)]];\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] = ((42*n + 12 + (219*n + 84)*x + (378*n + 219)*x^2 + (216*n + 252)*x^3 + 108*x^4)*v[i - 1])/(7*n - 5 + (12*n - 5)*x + 6*x^2)); 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-eed4f744ce063213","steps":["basis A013610","D+1"],"edges":["e-bf76d3591eaf645b","e-75dc0e851e137212"],"text":"A200536 \u2192 basis A013610 \u2192 D+1"},"headline":"A200536 \u2192 basis A013610 \u2192 D+1","chain":null}