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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:            289,            1394,              1681;\n  1:           4913,           35547,             85731,             68921;\n  2:          83521,          805732,           2914854,           4686628,            2825761;\n  3:        1419857,        17121805,          82587530,         199181690,          240189685,           115856201;\n  4:       24137569,       349284822,        2105982015,        6772177460,        12249673935,         11817332502,          4750104241;\n  5:      410338673,      6927482303,       50122371957,      201472279435,       485903732755,        703131283869,        565262404679,        194754273881;\n  6:     6975757441,    134591084744,     1136107097692,     5480046000632,     16520726913670,      31875284868728,      38437843518172,      26486581247816,       7984925229121;\n  7:   118587876497,   2574054495729,    24832055135268,   139741173016116,    505534243558302,    1219229646228846,    1960330019426772,    2026223465457924,    1221693560055513,     327381934393961;\n  8:  2015993900449,  48621029363770,   527681171624445,  3393714201819960,  14323470234151890,   41453807971780764,   83314025825637810,  114819329709282360,  103843952604718605,   55654928846973370,   13422659310152401;\n  9: 34271896307633, 909213249102499, 10964042121530135, 79328069467541565, 382641276255200490, 1291977015120500478, 3115944565878854094, 5367803663908950330, 6472939712360793045, 5203735847192010095, 2510037290998498987, 550329031716248441;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (17+58*x+41*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 289 + 1394*x + 1681*x^2.","mathematica":"P[0, x_] := 289 + 1394*x + 1681*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((17 + 58*x + 41*x^2)*P[n - 1, x])/(1 + x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 289 + 1394*x + 1681*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((17 + 58*x + 41*x^2)*v[i - 1])/(1 + 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-1f2dec04776afb2b","steps":["basis A013611","x \u21a6 x/(x+1)"],"edges":["e-5fcdd9bd1fb647dd","e-7261b50e45babe43"],"text":"A038320 \u2192 basis A013611 \u2192 x \u21a6 x/(x+1)"},"headline":"A038320 \u2192 basis A013611 \u2192 x \u21a6 x/(x+1)","chain":null}