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P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]"}]}],"used_by":[],"used_by_total":0,"links":[{"id":"l-3c508457d2bfbe13","kind":"oeis_match","node_a_id":"n-f96c16e0c5fd8334","node_b_id":null,"fingerprint":null,"oeis_id":"A009984","in_catalog":0,"target":"row_sums","row_alignment":null,"rows_matched":null,"oeis_nonn":1,"details":{"alignment":{"first_row":0,"low_zeros_dropped":false,"oeis_offset":0,"oeis_term_position":2,"target":"row_sums","terms_compared":15},"in_catalog":false,"oeis_id":"A009984","oeis_nonn":true},"other_id":null,"other":null}],"oeis":[{"oeis_id":"A009984","relation":"match_row_sums"}],"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:             361,              798,              441;\n  1:            6859,            22743,            25137,              9261;\n  2:          130321,           576156,           955206,            703836,            194481;\n  3:         2476099,         13683705,         30248190,          33432210,          18475695,           4084101;\n  4:        47045881,        311988474,        862073415,        1270423980,        1053114615,         465587514,          85766121;\n  5:       893871739,       6915744507,      22931152839,       42241597335,       46688081265,       30961569681,       11406894093,        1801088541;\n  6:     16983563041,     150170452152,     580922538588,     1284144558984,     1774147088070,     1568719530504,      866923951068,      273765458232,       37822859361;\n  7:    322687697779,    3209893414749,   14191107728364,    36598119931044,    60675830411994,    67062759929046,    49414665210876,    23406946678836,     6467708950731,      794280046581;\n  8:   6131066257801,   67764416533590,  337038808548645,   993377540985480,  1921401296379810,  2548384877303748,  2347196597516610,  1482439956326280,   614432350319445,   150913208850390,   16679880978201;\n  9: 116490258898219, 1416276305552031, 7826790109629645, 25951988258245665, 57367552991911470, 88768739892747222, 98112817776194298, 77457487718048130, 42805453738921335, 15770430324865755, 3486095124444009, 350277500542221;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (19+21*x)*P(n-1,x) for n >= 1, with P(0,x) = 361 + 798*x + 441*x^2.","mathematica":"P[0, x_] := 361 + 798*x + 441*x^2;\nP[n_, x_] := P[n, x] = Expand[(19 + 21*x)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 361 + 798*x + 441*x^2; for(n = 1, N, my(i = n + 1); v[i] = (19 + 21*x)*v[i - 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-5cf6acfdac607d6d","steps":["basis A013610"],"edges":["e-065a527a7a0e90c1"],"text":"A038333 \u2192 basis A013610"},"headline":"A038333 \u2192 basis A013610","chain":null}