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binomial(i,j)*11^(i-j)*7^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:           275,            252,             49;\n  1:          3872,           5775,           2646,            343;\n  2:         51909,         108416,          80850,          24696,           2401;\n  3:        673486,        1816815,        1897280,         943250,         216090,          16807;\n  4:       8535703,       28286412,       38153115,       26561920,        9904125,        1815156,         117649;\n  5:     106293660,      418249447,      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Expand[Together[((77*n + 275 + (49*n + 252)*x + 49*x^2)*P[n - 1, x])/(7*n + 18 + 7*x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 275 + 252*x + 49*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((77*n + 275 + (49*n + 252)*x + 49*x^2)*v[i - 1])/(7*n + 18 + 7*x)); 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-7dcf11eddf2b9a8a","steps":["D+1"],"edges":["e-e8839723596c882f"],"text":"A038321 \u2192 D+1"},"headline":"A038321 \u2192 D+1","chain":null}