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rows.","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:             0;\n  1:             2;\n  2:            26,             32;\n  3:           440,           1256,             864;\n  4:         10680,          49512,           74976,            36864;\n  5:        362680,        2355312,         5662776,          5956864,          2304000;\n  6:      16601560,      139372464,       463896408,        764030464,        621365760,        199065600;\n  7:     990347200,    10222528960,     43682572608,      98817320512,     124662019840,   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0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 0; v[2] = 2; for(n = 2, N, my(i = n + 1); v[i] = (-(n^6 - 4*n^5 + 8*n^4 - 8*n^3 + 4*n^2 + (4*n^6 - 16*n^5 + 28*n^4 - 24*n^3 + 8*n^2)*x + (4*n^6 - 16*n^5 + 24*n^4 - 16*n^3 + 4*n^2)*x^2)*v[i - 2] + (2*n^4 - 4*n^3 + 4*n^2 - 2*n + 1 + (4*n^4 - 8*n^3 + 4*n^2)*x)*v[i - 1])/(n^2 - 2*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-e734a631f8279507","steps":["basis A013609","D"],"edges":["e-031a48225080e193","e-36ce1da5a9a055ae"],"text":"A008955 \u2192 basis A013609 \u2192 D"},"headline":"A008955 \u2192 basis A013609 \u2192 D","chain":null}