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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: 0;\n 1: 24, 32;\n 2: 288, 1536, 2304, 1024;\n 3: 2592, 24192, 82944, 129024, 92160, 24576;\n 4: 20736, 276480, 1492992, 4202496, 6635520, 5898240, 2752512, 524288;\n 5: 155520, 2695680, 19906560, 81838080, 205701120, 327352320, 330301440, 204472320, 70778880, 10485760;\n 6: 1119744, 23887872, 223948800, 1214300160, 4220190720, 9852420096, 15755378688, 17270046720, 12740198400, 6039797760, 1660944384, 201326592;\n 7: 7838208, 198567936, 2257403904, 15216574464, 67722117120, 209799217152, 464932306944, 745952772096, 866843099136, 721378344960, 418557984768, 160658620416, 36641439744, 3758096384;\n 8: 53747712, 1576599552, 21069103104, 169890545664, 923027374080, 3574390063104, 10180947345408, 21703862255616, 34906105184256, 42363141488640, 38507334598656, 25773025001472, 12311523753984, 3968549781504, 773094113280, 68719476736;\n 9: 362797056, 12093235200, 185752092672, 1744005758976, 11196723363840, 52106901848064, 181844419018752, 485725669687296, 1004877543112704, 1619085565624320, 2032039222050816, 1976202499719168, 1472106483154944, 823113302409216, 333976656936960, 92771293593600, 15771119910912, 1236950581248;\n","recurrence_sentence":"The row polynomials satisfy (n-1)*P(n,x) = (6*n+24*n*x+16*n*x^2)*P(n-1,x) for n >= 2, with P(0,x) = 0, P(1,x) = 24 + 32*x.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 24 + 32*x;\nP[n_, x_] := P[n, x] = Expand[Together[((6*n + 24*n*x + 16*n*x^2)*P[n - 1, x])/(n - 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 0; v[2] = 24 + 32*x; for(n = 2, N, my(i = n + 1); v[i] = ((6*n + 24*n*x + 16*n*x^2)*v[i - 1])/(n - 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-d3c3090977105807","steps":["basis A013611","D"],"edges":["e-bced44278fba7ed1","e-26ee5b89b52e5c6b"],"text":"A272867 \u2192 basis A013611 \u2192 D"},"headline":"A272867 \u2192 basis A013611 \u2192 D","chain":null}