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 A361895 #19 Jul 11 2025 02:57:33
%S A361895 1,3,27,252,2487,25434,266364,2837082,30601233,333302931,3658565127,
%T A361895 40413860334,448778693844,5005642415907,56044616215041,
%U A361895 629552293867800,7092072533703567,80095810435943526,906605837653876254,10282430320166723448,116829834042508121682
%N A361895 Expansion of 1/(1 - 9*x/(1 - x)^3)^(1/3).
%H A361895 Winston de Greef, <a href="/A361895/b361895.txt">Table of n, a(n) for n = 0..932</a>
%F A361895 a(n) = Sum_{k=0..n} (-9)^k * binomial(-1/3,k) * binomial(n+2*k-1,n-k).
%F A361895 a(0) = 1; a(n) = (3/n) * Sum_{k=0..n-1} (n+2*k) * binomial(n+1-k,2) * a(k).
%F A361895 a(n) = 3*n*(1 + n)*hypergeom([1-n, 1+n/2, (3+n)/2], [5/3, 2], -4/3)/2 for n > 0. - _Stefano Spezia_, May 02 2024
%F A361895 a(n) ~ ((7 - sqrt(21))^(1/3) + (7 + sqrt(21))^(1/3))^(1/3) * (4 + (3*((39 - sqrt(21))/2))^(1/3) + (3*((39 + sqrt(21))/2))^(1/3))^n / (Gamma(1/3) * 2^(1/9) * 7^(2/9) * n^(2/3)). - _Vaclav Kotesovec_, Jul 11 2025
%t A361895 a[0]=1; a[n_]:=3*n*(1 + n)*HypergeometricPFQ[{1-n, 1+n/2, (3+n)/2}, {5/3, 2}, -4/3]/2; Array[a,21,0] (* _Stefano Spezia_, May 02 2024 *)
%o A361895 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-9*x/(1-x)^3)^(1/3))
%Y A361895 Cf. A004987, A361375, A361843, A361844, A361845, A361880, A361896.
%K A361895 nonn
%O A361895 0,2
%A A361895 _Seiichi Manyama_, Mar 28 2023