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 A361843 #18 Apr 07 2023 02:33:04
%S A361843 1,3,15,90,585,3969,27657,196290,1411965,10261485,75183147,554480316,
%T A361843 4111617510,30628393110,229048769790,1718666596692,12933847045701,
%U A361843 97584913269675,737953856289675,5591915004100950,42450848142844995,322796964495941235
%N A361843 Expansion of 1/(1 - 9*x*(1-x))^(1/3).
%H A361843 Winston de Greef, <a href="/A361843/b361843.txt">Table of n, a(n) for n = 0..1105</a>
%F A361843 n*a(n) = 3 * ( (3*n-2)*a(n-1) - (3*n-4)*a(n-2) ) for n > 1.
%F A361843 a(n) = (-1)^n * Sum_{k=0..n} 9^k * binomial(-1/3,k) * binomial(k,n-k).
%F A361843 a(n) = A004987(n)*hypergeom([1/2 - n/2, -n/2], [2/3 - n], 4/9). - _Peter Luschny_, Mar 27 2023
%F A361843 a(n) ~ 3^n * phi^(2*n + 2/3) / (Gamma(1/3) * 5^(1/6) * n^(2/3)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Mar 29 2023
%p A361843 A361843 := n -> (-9)^n*binomial(-1/3, n)*hypergeom([1/2 - n/2, -n/2], [2/3 - n], 4/9): seq(simplify(A361843(n)), n = 0..21); # _Peter Luschny_, Mar 27 2023
%o A361843 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-9*x*(1-x))^(1/3))
%Y A361843 Column k=1 of A361840.
%Y A361843 Cf. A004987.
%K A361843 nonn
%O A361843 0,2
%A A361843 _Seiichi Manyama_, Mar 26 2023