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binomial(j, n-k) * |Stirling1(n, n-j)|.","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:         4,          3;\n  2:        18,         51,          18;\n  3:       117,        552,         711,          162;\n  4:       999,       6492,       14301,        11610,         1944;\n  5:     10566,      86823,      268074,       376515,       220806,        29160;\n  6:    133236,    1318419,     5206446,     10343835,     10556244,      4820148,       524880;\n  7:   1950363,   22517064,   107924166,    276065820,    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+ 18*n)*x + (9*n^3 - 18*n^2 + 9*n)*x^2)*v[i - 2] + (4*n^2 - 6*n + 1 + (6*n^2 - 6*n)*x)*v[i - 1])/(n - 1)); 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-849de7332df28657","steps":["basis A013610","D+1"],"edges":["e-678ee1ecc620a9a6","e-50cc5acbf864506d"],"text":"A088996 \u2192 basis A013610 \u2192 D+1"},"headline":"A088996 \u2192 basis A013610 \u2192 D+1","chain":null}