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reverse","chain":null}}],"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:        6,        11;\n  2:       36,       132,        121;\n  3:      216,      1188,       2178,       1331;\n  4:     1296,      9504,      26136,      31944,       14641;\n  5:     7776,     71280,     261360,     479160,      439230,      161051;\n  6:    46656,    513216,    2352240,    5749920,     7906140,     5797836,     1771561;\n  7:   279936,   3592512,   19758816,   60374160,   110685960,   121754556,    74405562,    19487171;\n  8:  1679616,  24634368,  158070528,  579591936,  1328231520,  1948072896,  1785733488,   935384208,   214358881;\n  9: 10077696, 166281984, 1219401216, 5216327424, 14344900416, 26298984096, 32143202784, 25255373616, 11575379574, 2357947691;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (6+17*x+11*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[((6 + 17*x + 11*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] = ((6 + 17*x + 11*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-e6ebe74518d42cbe","steps":["x \u21a6 x/(x+1)"],"edges":["e-afe3a450266622c8"],"text":"A038259 \u2192 x \u21a6 x/(x+1)"},"headline":"A038259 \u2192 x \u21a6 x/(x+1)","chain":null}