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(1+6x)^n.","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 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:         1;\n  1:        25,          18;\n  2:       301,         900,          324;\n  3:      2989,       16254,        24300,         5832;\n  4:     27097,      215208,       585144,       583200,        104976;\n  5:    232897,     2438730,      9684360,     17554320,      13122000,       1889568;\n  6:   1932805,    25152876,    131691420,    348636960,     473966640,     283435200,      34012224;\n  7:  15647317,   243533430,   1584631188,   5531039640,   10982064240,   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v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-b7cf68162d40a956","steps":["x \u21a6 x/(x+1)","D+1"],"edges":["e-149dcf3d57e14e87","e-d284dbad9e86564e"],"text":"A038277 \u2192 x \u21a6 x/(x+1) \u2192 D+1"},"headline":"A038277 \u2192 x \u21a6 x/(x+1) \u2192 D+1","chain":null}