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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: 24, 36, 9;\n 2: 252, 1080, 1404, 648, 81;\n 3: 2160, 15552, 41796, 52488, 32076, 8748, 729;\n 4: 16848, 171072, 707616, 1539648, 1907064, 1364688, 542376, 104976, 6561;\n 5: 124416, 1632960, 9156240, 28693440, 55287360, 68024448, 53800200, 26768880, 7873200, 1180980, 59049;\n 6: 886464, 14276736, 101196864, 415704960, 1097524080, 1953813312, 2395342368, 2029396032, 1172713140, 446410440, 104162436, 12754584, 531441;\n 7: 6158592, 117573120, 1008189504, 5132066688, 17274430656, 40553908416, 68284263600, 83545359552, 74421580464, 47855199168, 21740188428, 6696156600, 1294590276, 133923132, 4782969;\n 8: 41990400, 927148032, 9331946496, 56717273088, 232477330176, 679972382208, 1465019861760, 2366978692608, 2892518571744, 2676830053248, 1864924254144, 964246550400, 360521071344, 93210499872, 15382028304, 1377495072, 43046721;\n 9: 282175488, 7074542592, 81765386496, 577935710208, 2794988519424, 9805316032512, 25818951336192, 52095026962944, 81529341661440, 99559833823872, 94941092847456, 70401018139776, 40189796220672, 17356437907200, 5510669035536, 1227348109152, 176663742984, 13947137604, 387420489;\n","recurrence_sentence":"The row polynomials satisfy (6*n-4+6*n*x+3*x^2)*P(n,x) = (36*n+12+(144*n+72)*x+(162*n+144)*x^2+(54*n+108)*x^3+27*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[((36*n + 12 + (144*n + 72)*x + (162*n + 144)*x^2 + (54*n + 108)*x^3 + 27*x^4)*P[n - 1, x])/(6*n - 4 + 6*n*x + 3*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] = ((36*n + 12 + (144*n + 72)*x + (162*n + 144)*x^2 + (54*n + 108)*x^3 + 27*x^4)*v[i - 1])/(6*n - 4 + 6*n*x + 3*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-d3c3090977105807","steps":["basis A013610","D+1"],"edges":["e-0f2bf5edb3121755","e-ffe475ee7ebb9b63"],"text":"A272867 \u2192 basis A013610 \u2192 D+1"},"headline":"A272867 \u2192 basis A013610 \u2192 D+1","chain":null}