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 A377260 #9 May 03 2025 03:59:51
%S A377260 1,12,138,1512,16191,170856,1785042,18514548,190978047,1961435736,
%T A377260 20074741596,204870399552,2085761241018,21191569851312,
%U A377260 214930928188116,2176565295933000,22012171108148025,222351327936731700,2243667436429422150,22618648367553735000,227826739721910301245
%N A377260 Expansion of 1/(1 - 9*x*(1 + x))^(4/3).
%F A377260 a(n) = 3*((3*n+1)*a(n-1) + (3*n+2)*a(n-2))/n for n > 1.
%F A377260 a(n) = Sum_{k=0..n} (-9)^k * binomial(-4/3,k) * binomial(k,n-k).
%F A377260 a(n) ~ n^(1/3) * 3^(n+1) * (3 + sqrt(13))^(n + 4/3) / (13^(2/3) * Gamma(1/3) * 2^(n + 4/3)). - _Vaclav Kotesovec_, May 03 2025
%o A377260 (PARI) a(n) = sum(k=0, n, (-9)^k*binomial(-4/3, k)*binomial(k, n-k));
%Y A377260 Cf. A180400, A376568, A377261.
%Y A377260 Cf. A377234.
%K A377260 nonn
%O A377260 0,2
%A A377260 _Seiichi Manyama_, Oct 21 2024