A376802
Expansion of 1/((1 - x)^3 - 9*x)^(1/3).
Original entry on oeis.org
1, 4, 31, 283, 2770, 28204, 294568, 3131650, 33732883, 367035814, 4025600941, 44439461275, 493218155119, 5498860571026, 61543476786067, 691095770653867, 7783168304357434, 87878978740300960, 994484816394177214, 11276915136560900662, 128106749179069022344
Offset: 0
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CoefficientList[Series[1/Surd[((1-x)^3-9x),3],{x,0,30}],x] (* Harvey P. Dale, Dec 11 2024 *)
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my(N=30, x='x+O('x^N)); Vec(1/((1-x)^3-9*x)^(1/3))
A376806
Expansion of 1/((1 - x^3)^3 - 9*x)^(1/3).
Original entry on oeis.org
1, 3, 18, 127, 957, 7497, 60229, 492483, 4079826, 34138873, 287946771, 2444458878, 20863127251, 178868929074, 1539439262406, 13293346718161, 115123998810525, 999553370761017, 8698196146639573, 75845560146124527, 662551474429229571, 5797239969198654748
Offset: 0
A383598
Expansion of 1/( (1-x^2)^2 * (1-x^2-9*x) )^(1/3).
Original entry on oeis.org
1, 3, 19, 132, 1000, 7884, 63802, 525666, 4388518, 37010220, 314633944, 2692239012, 23161121641, 200158043223, 1736461678195, 15114944308560, 131950690469920, 1154858014686960, 10130508263000440, 89045875688728440, 784127521246844872, 6916291864328172336
Offset: 0
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R:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/( (1-x^2)^2 * (1-x^2-9*x) )^(1/3))); // Vincenzo Librandi, May 04 2025
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Table[Sum[(-9)^(n-2*k)* Binomial[-1/3, n-2*k]* Binomial[n-k,k],{k,0,Floor[n/2]}],{n,0,22}] (* Vincenzo Librandi, May 04 2025 *)
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a(n) = sum(k=0, n\2, (-9)^(n-2*k)*binomial(-1/3, n-2*k)*binomial(n-k, k));
Showing 1-3 of 3 results.