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A108733
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Expansion of (1+18*x)^(1/3).
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4
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1, 6, -36, 360, -4320, 57024, -798336, 11632896, -174493440, 2675566080, -41738830848, 660232415232, -10563718643712, 170644685783040, -2779070597038080, 45576757791424512, -752016503558504448, 12474626706088132608, -207910445101468876800, 3479764291698268569600
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1-18*x)^(1/3) = 1 + 6*x/(G(0)-6*x) where G(k)= k*(1-18*x) + 1+ 6*x + 6*x*(k+1)*(3*k+2)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Jul 06 2012
a(n) ~ -(-1)^n * 2^n * 3^(2*n-1) / (Gamma(2/3) * n^(4/3)). - Vaclav Kotesovec, Jun 16 2018
D-finite with recurrence: n*a(n) +6*(3*n-4)*a(n-1)=0. - R. J. Mathar, Jan 20 2020
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MATHEMATICA
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CoefficientList[Series[(1 + 18 x)^(1/3), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 21 2020 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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