This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A098536 #27 Oct 04 2024 14:21:17
%S A098536 1,1,1,1,4,13,31,61,124,295,757,1873,4402,10237,24421,59701,146455,
%T A098536 356308,862810,2096632,5127391,12583513,30886735,75775729,186054142,
%U A098536 457662265,1127659903,2781162079,6862930768,16945704721,41876228125,103573882633,256359901387,634900971064
%N A098536 Expansion of 1/((1-x)^3 - 9*x^4)^(1/3).
%C A098536 Binomial transform of A098535.
%H A098536 G. C. Greubel, <a href="/A098536/b098536.txt">Table of n, a(n) for n = 0..1000</a>
%F A098536 Recurrence: n*a(n) +(-3*n+2)*a(n-1) +(3*n-4)*a(n-2) +(-n+2)*a(n-3) + 3*(-3*n+8)*a(n-4)=0. - _R. J. Mathar_, Nov 10 2014
%F A098536 a(n) = Sum_{k=0..floor(n/4)} (-9)^k * binomial(-1/3,k) * binomial(n-k,n-4*k). - _Seiichi Manyama_, Oct 04 2024
%p A098536 with(FormalPowerSeries): # requires Maple 2022
%p A098536 re:= subs(n=n-1, FindRE(1/((1-x)^3 - 9*x^4)^(1/3), x, a(n)));
%p A098536 # re = Mathar's recurrence
%p A098536 f:= gfun:-rectoproc({re, a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=4}, a(n), remember): map(f, [$0..30]); # _Georg Fischer_, Oct 23 2022
%t A098536 CoefficientList[Series[1/((1-x)^3-9*x^4)^(1/3),{x,0,40}],x] (* _Harvey P. Dale_, May 11 2011 *)
%o A098536 (PARI) x='x+O('x^30); Vec(1/((1-x)^3-9*x^4)^(1/3)) \\ _G. C. Greubel_, Jan 17 2018
%o A098536 (Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q,30); Coefficients(R!(1/((1-x)^3-9*x^4)^(1/3))); // _G. C. Greubel_, Jan 17 2018
%Y A098536 Cf. A098535, A098538.
%K A098536 easy,nonn
%O A098536 0,5
%A A098536 _Paul Barry_, Sep 13 2004