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grid by dominoes, 2k of which are in a vertical position (0<=k<=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:       42,        72;\n  1:      228,       792,        648;\n  2:     1116,      5832,       9720,        5184;\n  3:     5154,     35928,      90720,       98496,       38880;\n  4:    22926,    199728,     676512,     1114560,      894240,       279936;\n  5:    99336,   1038096,    4412880,     9771840,    11897280,      7558272,      1959552;\n  6:   422136,   5144688,   26317872,    73275840,   119983680,    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+ 1); v[i] = ((4*n^2 + 19*n + 21 + (6*n^2 + 30*n + 36)*x)*v[i - 1] + (2*n + 4 + (8*n + 16)*x + (6*n + 12)*x^2)*deriv(v[i - 1], x))/(2*n^2 + 5*n + 3)); 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-8eb9bb3a09f0b7fd","steps":["basis A013610","D"],"edges":["e-8cd26e1d1ff01e6d","e-2ff926af7fc2f763"],"text":"A123519 \u2192 basis A013610 \u2192 D"},"headline":"A123519 \u2192 basis A013610 \u2192 D","chain":null}