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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:       28,        32;\n  1:      152,       352,        192;\n  2:      744,      2592,       2880,       1024;\n  3:     3436,     15968,      26880,      19456,       5120;\n  4:    15284,     88768,     200448,     220160,     117760,      24576;\n  5:    66224,    461376,    1307520,    1930240,    1566720,     663552,     114688;\n  6:   281424,   2286528,    7797888,   14474240,   15800320,   10149888,    3555328,     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1] + (3*n + 6 + (8*n + 16)*x + (4*n + 8)*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 A013609","D"],"edges":["e-125a67b606fd2347","e-81f5be5a34f4af6f"],"text":"A123519 \u2192 basis A013609 \u2192 D"},"headline":"A123519 \u2192 basis A013609 \u2192 D","chain":null}