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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:             361,             1254,              1089;\n  1:            6859,            35739,             62073,              35937;\n  2:          130321,           905388,           2358774,            2731212,            1185921;\n  3:         2476099,         21502965,          74694510,          129732570,          112662495,           39135393;\n  4:        47045881,        490267602,        2128793535,         4929837660,         6421762215,         4461434802,          1291467969;\n  5:       893871739,      10867598511,       56625908031,       163917102195,       284698124865,       296685414333,        171765239877,         42618442977;\n  6:     16983563041,     235982139096,     1434523003452,      4983079906728,     10818528744870,     15032060992872,      13054158230652,       6478003332504,       1406408618241;\n  7:    322687697779,    5044118223177,    35043347655756,    142017777341748,    369993683074554,    642620607445278,     744087019147164,     553869284929092,     240495873719211,     46411484401953;\n  8:   6131066257801,  106486940267070,   832279506824205,   3854768242133160,  11716466630694210,  24419583082920564,   35344133409490290,   35078388045509160,   22847108003325045,   8818182036371070,   1531578985264449;\n  9: 116490258898219, 2225577051581763, 19327379658473205, 100705820325728805, 349820217973584270, 850615477388399646, 1477384776516694122, 1832845775377853610, 1591681857564978135, 921500022800776815, 320100007920269841, 50542106513726817;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (19+52*x+33*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 361 + 1254*x + 1089*x^2.","mathematica":"P[0, x_] := 361 + 1254*x + 1089*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((19 + 52*x + 33*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] = 361 + 1254*x + 1089*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((19 + 52*x + 33*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-5cf6acfdac607d6d","steps":["basis A013609","x \u21a6 x/(x+1)"],"edges":["e-20f4338b8f3f0a8d","e-ef2295369865097d"],"text":"A038333 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)"},"headline":"A038333 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)","chain":null}