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 A361844 #17 Mar 27 2023 15:14:13
%S A361844 1,3,12,57,297,1629,9216,53217,311796,1846818,11032416,66356712,
%T A361844 401364531,2439135585,14882263002,91116281565,559528781697,
%U A361844 3445002647847,21260140172244,131474746842345,814564464082263,5055177167348463,31420067723814780
%N A361844 Expansion of 1/(1 - 9*x*(1-x)^2)^(1/3).
%H A361844 Seiichi Manyama, <a href="/A361844/b361844.txt">Table of n, a(n) for n = 0..1000</a>
%F A361844 n*a(n) = 3 * ( (3*n-2)*a(n-1) - 2*(3*n-4)*a(n-2) + (3*n-6)*a(n-3) ) for n > 2.
%F A361844 a(n) = (-1)^n * Sum_{k=0..n} 9^k * binomial(-1/3,k) * binomial(2*k,n-k).
%F A361844 a(n) = (-9)^n*binomial(-1/3, n)*hypergeom([1/3 - n*2/3, 2/3 - n*2/3, -n*2/3], [1/2 - n, 2/3 - n], 3/4). - _Peter Luschny_, Mar 27 2023
%p A361844 A361844 := n -> (-9)^n*binomial(-1/3, n)*hypergeom([1/3 - n*2/3, 2/3 - n*2/3,
%p A361844 -n*2/3], [1/2 - n, 2/3 - n], 3/4):
%p A361844 seq(simplify(A361844(n)), n = 0..22); # _Peter Luschny_, Mar 27 2023
%o A361844 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-9*x*(1-x)^2)^(1/3))
%Y A361844 Column k=2 of A361840.
%Y A361844 Cf. A361815, A004987.
%K A361844 nonn
%O A361844 0,2
%A A361844 _Seiichi Manyama_, Mar 26 2023