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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:           169,            494,             361;\n  1:          2197,           9633,           14079,            6859;\n  2:         28561,         166972,          366054,          356668,           130321;\n  3:        371293,        2713295,         7931170,        11591710,          8470865,          2476099;\n  4:       4826809,       42327402,       154657815,       301384460,        330363735,        193135722,         47045881;\n  5:      62748517,      641965597,      2814772233,      6856496465,      10021033295,       8787675351,       4281175171,        893871739;\n  6:     815730721,     9537774584,     48789385372,    142615126472,     260546865670,     304639412168,     222621108892,      92962660856,      16983563041;\n  7:   10604499373,   139489953291,    815479726932,   2780994966204,    6096796656678,    8910702805914,    8682223246788,    5438315660076,    1987076875797,     322687697779;\n  8:  137858491849,  2014854880870,  13251545562645,  51647049372360,  132097260894690,  231678272953764,  282172255520610,  235660345269960,  129159996926805,   41949400711270,   6131066257801;\n  9: 1792160394037, 28812424796441, 210552335050915, 923191007530935, 2698558329705810, 5521665505398042, 8070126507889446, 8424857343401070, 6156626520177705, 2999382150855805, 876742474865543, 116490258898219;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (13+32*x+19*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 169 + 494*x + 361*x^2.","mathematica":"P[0, x_] := 169 + 494*x + 361*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((13 + 32*x + 19*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] = 169 + 494*x + 361*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((13 + 32*x + 19*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-4397e742863fdbe2","steps":["basis A013609","x \u21a6 x/(x+1)"],"edges":["e-54bb49968ded72d0","e-9abbc1f3b5974fea"],"text":"A038305 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)"},"headline":"A038305 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)","chain":null}