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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: 30, 56, 16;\n 2: 324, 1824, 3072, 1792, 256;\n 3: 2808, 26784, 95040, 156672, 124416, 43008, 4096;\n 4: 22032, 297216, 1631232, 4700160, 7686144, 7225344, 3735552, 917504, 65536;\n 5: 163296, 2851200, 21254400, 88473600, 226160640, 368492544, 384860160, 251658240, 96337920, 18350080, 1048576;\n 6: 1166400, 25007616, 235892736, 1288949760, 4523765760, 10696458240, 17397448704, 19520815104, 14898954240, 7455375360, 2264924160, 352321536, 16777216;\n 7: 8118144, 206406144, 2356687872, 15969042432, 71526260736, 223343640576, 499898843136, 812371673088, 960087195648, 817694244864, 490695819264, 198709346304, 50029658112, 6576668672, 268435456;\n 8: 55427328, 1630347264, 21857402880, 176913580032, 965500010496, 3758995537920, 10776679022592, 23158283304960, 37619087966208, 46241597620224, 42743648747520, 29273691783168, 14459275837440, 4915590070272, 1056561954816, 120259084288, 4294967296;\n 9: 372874752, 12456032256, 191798710272, 1805923123200, 11632724803584, 54346246520832, 190528902660096, 511703443832832, 1065593251823616, 1730738625970176, 2193947778613248, 2160933338087424, 1636790024798208, 936352262651904, 392770464251904, 115036404056064, 21569325760512, 2164663517184, 68719476736;\n","recurrence_sentence":"The row polynomials satisfy (12*n-9+(16*n-4)*x+8*x^2)*P(n,x) = (72*n+18+(384*n+144)*x+(576*n+384)*x^2+(256*n+384)*x^3+128*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[((72*n + 18 + (384*n + 144)*x + (576*n + 384)*x^2 + (256*n + 384)*x^3 + 128*x^4)*P[n - 1, x])/(12*n - 9 + (16*n - 4)*x + 8*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] = ((72*n + 18 + (384*n + 144)*x + (576*n + 384)*x^2 + (256*n + 384)*x^3 + 128*x^4)*v[i - 1])/(12*n - 9 + (16*n - 4)*x + 8*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 A013611","D+1"],"edges":["e-bced44278fba7ed1","e-8154acea9f93827a"],"text":"A272867 \u2192 basis A013611 \u2192 D+1"},"headline":"A272867 \u2192 basis A013611 \u2192 D+1","chain":null}