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 A372039 #15 Apr 19 2024 05:19:46
%S A372039 1,3,-6,27,-144,837,-5139,32778,-215001,1440747,-9818820,67834665,
%T A372039 -473945580,3342743235,-23766448545,170148578130,-1225477405485,
%U A372039 8873126329095,-64547392633740,471509782020405,-3457212506428230,25434642838306185,-187694935991201745
%N A372039 Expansion of ( 1 + 9*x*(1 + x) )^(1/3).
%F A372039 a(n) = Sum_{k=0..n} 9^k * binomial(1/3,k) * binomial(k,n-k).
%F A372039 a(n) ~ (-1)^(n+1) * Gamma(1/3) * 5^(1/6) * 3^(n - 1/2) * phi^(2*n - 2/3) / (2*Pi*n^(4/3)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Apr 19 2024
%o A372039 (PARI) my(N=30, x='x+O('x^N)); Vec((1+9*x*(1+x))^(1/3))
%o A372039 (PARI) a(n) = sum(k=0, n, 9^k*binomial(1/3, k)*binomial(k, n-k));
%Y A372039 Cf. A180400, A361843, A372024, A372038.
%K A372039 sign
%O A372039 0,2
%A A372039 _Seiichi Manyama_, Apr 16 2024