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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:         12,          22;\n  2:        144,         528,          484;\n  3:       1728,        9504,        17424,         10648;\n  4:      20736,      152064,       418176,        511104,        234256;\n  5:     248832,     2280960,      8363520,      15333120,      14055360,        5153632;\n  6:    2985984,    32845824,    150543360,     367994880,     505992960,      371061504,      113379904;\n  7:   35831808,   459841536,   2529128448,    7727892480,   14167802880,    15584583168,     9523911936,     2494357888;\n  8:  429981696,  6306398208,  40466055168,  148375535616,  340027269120,   498706661376,   457147772928,   239458357248,   54875873536;\n  9: 5159780352, 85136375808, 624333422592, 2670759641088, 7344589012992, 13465079857152, 16457319825408, 12930751291392, 5926594341888, 1207269217792;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (12+34*x+22*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[((12 + 34*x + 22*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] = ((12 + 34*x + 22*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-a6a633b989da1879","steps":["basis A013609","x \u21a6 x/(x+1)"],"edges":["e-e169cb33ba7b2c8c","e-abc8fe4c398b38d7"],"text":"A038271 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)"},"headline":"A038271 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)","chain":null}