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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,            1258,             1369;\n  1:           4913,           32079,            69819,             50653;\n  2:          83521,          727124,          2373846,           3444404,            1874161;\n  3:        1419857,        15451385,         67258970,         146387170,          159303685,           69343957;\n  4:       24137569,       315208254,       1715103735,        4977163780,         8124487935,         7073083614,          2565726409;\n  5:      410338673,      6251630371,      40819468893,      148070622455,       322271354755,       420848475033,        305321442671,         94931877133;\n  6:     6975757441,    121460247208,     925241294908,     4027520930776,     10957226061670,     19078464201496,      20761858101628,      12910735290088,       3512479453921;\n  7:   118587876497,   2322927227853,   20223131160132,   102701783734788,    335291117487102,    729751255707222,    1058854763183028,     987671249691732,     537409356449913,     129961739795077;\n  8:  2015993900449,  43877514303890,  429741537152805,  2494186176416280,   9499914995467890,  24811542694045548,   45001327435278690,   55968037482531480,   45679795298242605,   22093495765163090,   4808584372417849;\n  9: 34271896307633, 820509517482743, 8929074160841615, 58301601873730545, 253783443450356490, 773293080631086246, 1683049646079423006, 2616505752308346690, 2847373906923789045, 2065741854042748915, 899205277642137763, 177917621779460413;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (17+54*x+37*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 289 + 1258*x + 1369*x^2.","mathematica":"P[0, x_] := 289 + 1258*x + 1369*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((17 + 54*x + 37*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 + 1258*x + 1369*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((17 + 54*x + 37*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-a5302200d285579d","steps":["basis A013611","x \u21a6 x/(x+1)"],"edges":["e-df900b884626232f","e-e4c4d29b1f8dc32e"],"text":"A038331 \u2192 basis A013611 \u2192 x \u21a6 x/(x+1)"},"headline":"A038331 \u2192 basis A013611 \u2192 x \u21a6 x/(x+1)","chain":null}