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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-42ac62a61d6e0c98","kind":"oeis_match","node_a_id":"n-c21cdce554fb6206","node_b_id":null,"fingerprint":null,"oeis_id":"A009979","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":"A009979","oeis_nonn":true},"other_id":null,"other":null}],"oeis":[{"oeis_id":"A009979","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:            289,             612,              324;\n  1:           4913,           15606,            16524,             5832;\n  2:          83521,          353736,           561816,           396576,            104976;\n  3:        1419857,         7516890,         15918120,         16854480,           8922960,           1889568;\n  4:       24137569,       153344556,        405912060,        573052320,         455070960,         192735936,          34012224;\n  5:      410338673,      3041333694,       9660707028,      17048306520,       18051148080,       11467788192,        4047454656,         612220032;\n  6:     6975757441,     59088768912,     218976025968,     463713937344,      613739034720,      519873064704,      275226916608,       83261924352,      11019960576;\n  7:   118587876497,   1130072705442,    4786190281872,   11824705402272,    18780414462432,    19885144724928,    14036572747008,     6369537212928,    1686053968128,     198359290368;\n  8:  2015993900449,  21345817769460,  101706543489780,  287171416912320,   532111743102240,   676094920647552,   596554341747840,   360940442065920,  143314587290880,   33721079362560,   3570467226624;\n  9: 34271896307633, 399166792288902, 2113235959176540, 6712631870325480, 14214985137159840, 21071625026848704, 22311132381369216, 16873965666581760, 8933275941131520, 3152920920399360, 667677371378688, 64268410079232;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (17+18*x)*P(n-1,x) for n >= 1, with P(0,x) = 289 + 612*x + 324*x^2.","mathematica":"P[0, x_] := 289 + 612*x + 324*x^2;\nP[n_, x_] := P[n, x] = Expand[(17 + 18*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] = 289 + 612*x + 324*x^2; for(n = 1, N, my(i = n + 1); v[i] = (17 + 18*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-1f2dec04776afb2b","steps":["basis A013610"],"edges":["e-572c9115d911d6cf"],"text":"A038320 \u2192 basis A013610"},"headline":"A038320 \u2192 basis A013610","chain":null}