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))
A383599
Expansion of 1/( (1-x^3)^2 * (1-x^3-9*x) )^(1/3).
Original entry on oeis.org
1, 3, 18, 127, 951, 7425, 59473, 484902, 4005720, 33425587, 281152551, 2380227705, 20259341335, 173218395228, 1486747223136, 12803424371263, 110579924167533, 957494150283249, 8309596928695417, 72260720257071936, 629526082305028041, 5493357757059584986
Offset: 0
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R:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/( (1-x^3)^2 * (1-x^3-9*x) )^(1/3))); // Vincenzo Librandi, May 04 2025
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Table[Sum[(-9)^(n-3*k)* Binomial[-1/3, n-3*k]* Binomial[n-2*k,k],{k,0,Floor[n/3]}],{n,0,22}] (* Vincenzo Librandi, May 04 2025 *)
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a(n) = sum(k=0, n\3, (-9)^(n-3*k)*binomial(-1/3, n-3*k)*binomial(n-2*k, k));
A376805
Expansion of 1/((1 - x^2)^3 - 9*x)^(1/3).
Original entry on oeis.org
1, 3, 19, 138, 1072, 8661, 71758, 605094, 5169286, 44605527, 387969346, 3396331158, 29891385937, 264264469542, 2345319267553, 20883723678234, 186497307222706, 1669724703219384, 14983025158691938, 134719748524295094, 1213531265862339751
Offset: 0
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