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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:       56,       128;\n  1:      304,      1408,       1536;\n  2:     1488,     10368,      23040,       16384;\n  3:     6872,     63872,     215040,      311296,       163840;\n  4:    30568,    355072,    1603584,     3522560,      3768320,      1572864;\n  5:   132448,   1845504,   10460160,    30883840,     50135040,     42467328,      14680064;\n  6:   562848,   9146112,   62383104,   231587840,    505610240,    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+ 128*x; for(n = 1, N, my(i = n + 1); v[i] = ((8*n^2 + 38*n + 42 + (16*n^2 + 80*n + 96)*x)*v[i - 1] + (3*n + 6 + (16*n + 32)*x + (16*n + 32)*x^2)*deriv(v[i - 1], x))/(4*n^2 + 10*n + 6)); 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 A013611","D"],"edges":["e-ab96494d3bfaa8ca","e-6f94aa17f1db9c80"],"text":"A123519 \u2192 basis A013611 \u2192 D"},"headline":"A123519 \u2192 basis A013611 \u2192 D","chain":null}