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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:            23,             47;\n  2:           529,           2162,            2209;\n  3:         12167,          74589,          152421,           103823;\n  4:        279841,        2287396,         7011366,          9551716,          4879681;\n  5:       6436343,       65762635,       268769030,        549223670,        561163315,        229345007;\n  6:     148035889,     1815048726,      9272531535,      25264288820,      38720268735,      31649610966,       10779215329;\n  7:    3404825447,    48703807481,    298575515427,    1016887625005,    2077987755445,    2547793682763,     1735453667969,     506623120463;\n  8:   78310985281,  1280214368072,   9156315806428,   37421464600184,   95587436750470,  156264679209464,   159661737453148,   93218654165192,   23811286661761;\n  9: 1801152661463, 33125546773863, 270765338847228, 1291040528706348, 3957319881469458, 8086697149089762, 11016659884267212, 9648130706097372, 4928936338984527, 1119130473102767;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (23+70*x+47*x^2)*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[((23 + 70*x + 47*x^2)*P[n - 1, x])/(1 + x)]];\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] = ((23 + 70*x + 47*x^2)*v[i - 1])/(1 + x)); 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-9e472291b944d56e","steps":["basis A013609","x \u21a6 x/(x+1)"],"edges":["e-15af34f262d68ea6","e-50d07eea4f1d4fee"],"text":"A038326 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)"},"headline":"A038326 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)","chain":null}