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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:            289,             986,              841;\n  1:           4913,           25143,            42891,             24389;\n  2:          83521,          569908,          1458294,           1658452,            707281;\n  3:        1419857,        12110545,         41318330,          70484210,          60118885,           20511149;\n  4:       24137569,       247055118,       1053617415,        2396463140,        3066063135,         2092137198,          594823321;\n  5:      410338673,      4899926507,      25076094477,       71294778415,      121620504355,       124482163281,        70783975199,        17249876309;\n  6:     6975757441,     95198572136,     568391474812,     1939217972888,     4135097148070,      5643191402072,      4813310313532,      2345983178024,       500246412961;\n  7:   118587876497,   1820672692101,   12423413663748,    49450058308644,   126533972730942,    215852071129254,    245478825990132,    179467713118836,     76537701183033,     14507145975869;\n  8:  2015993900449,  34390484184130,  263997540354645,  1200929987495640,  3585129227376690,   7338970418394636,  10432850104580610,  10169837076734040,   6505704600557805,   2466214815897730,   420707233300201;\n  9: 34271896307633, 643102054243231, 5485282227368735, 28071738457710585, 95774166502777290, 228731244706632822, 390188593911314814, 475439883337316370, 405522253434769845, 230591085286437755, 78672252627137587, 12200509765705829;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (17+46*x+29*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 289 + 986*x + 841*x^2.","mathematica":"P[0, x_] := 289 + 986*x + 841*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((17 + 46*x + 29*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] = 289 + 986*x + 841*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((17 + 46*x + 29*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-1f2dec04776afb2b","steps":["basis A013609","x \u21a6 x/(x+1)"],"edges":["e-7304be3f66cc3caf","e-8eaacc26f8b3d0a2"],"text":"A038320 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)"},"headline":"A038320 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)","chain":null}