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A049146
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Revert transform of (1 + 3x - x^3)/(1 + 4x + 4x^2 + 2x^3).
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0
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1, 1, 2, 4, 10, 24, 66, 173, 498, 1378, 4070, 11680, 35078, 103292, 313980, 942133, 2890878, 8798182, 27204516, 83704806, 260493354, 808445448, 2529836520, 7906101138, 24858833998, 78131339008, 246694899708, 779057755912
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OFFSET
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1,3
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LINKS
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FORMULA
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Recurrence: 81*(n-2)*(n-1)*n*(1813084*n^6 - 45013004*n^5 + 455841450*n^4 - 2406545725*n^3 + 6968759906*n^2 - 10457422881*n + 6322174470)*a(n) = - 108*(n-2)*(n-1)*(1813084*n^7 - 47732630*n^6 + 524234975*n^5 - 3106796865*n^4 + 10703694351*n^3 - 21382966105*n^2 + 22875924945*n - 10080872550)*a(n-1) + 12*(n-2)*(125102796*n^8 - 3606308460*n^7 + 44406583604*n^6 - 305044684570*n^5 + 1278696097644*n^4 - 3351074201645*n^3 + 5368355075446*n^2 - 4816013331765*n + 1857131824050)*a(n-2) + 8*(335420540*n^9 - 10843059790*n^8 + 152744811074*n^7 - 1229343861889*n^6 + 6220523112425*n^5 - 20479834354645*n^4 + 43743928459836*n^3 - 58213329297171*n^2 + 43536111721020*n - 13816964175300)*a(n-3) + 16*(n-5)*(1813084*n^8 - 52265340*n^7 + 664619479*n^6 - 4509800628*n^5 + 16009699681*n^4 - 20818559775*n^3 - 36865773969*n^2 + 145742743728*n - 125931131460)*a(n-4) - 48*(n-6)*(n-5)*(14504672*n^7 - 352851696*n^6 + 3575308748*n^5 - 19443403045*n^4 + 60795306088*n^3 - 107957844569*n^2 + 98758778272*n - 34586854140)*a(n-5) + 176*(n-7)*(n-6)*(n-5)*(1813084*n^6 - 34134500*n^5 + 257972690*n^4 - 997048285*n^3 + 2061237651*n^2 - 2130360960*n + 839607300)*a(n-6). - Vaclav Kotesovec, Jan 02 2021
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MATHEMATICA
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Rest[CoefficientList[InverseSeries[Series[x*(1 + 3x - x^3)/(1 + 4x + 4x^2 + 2x^3), {x, 0, 40}], x], x]] (* Vaclav Kotesovec, Jan 02 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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