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 A377261 #9 May 03 2025 04:07:16
%S A377261 1,15,195,2340,26910,301158,3307590,35830080,384072975,4082949585,
%T A377261 43113860361,452742067440,4732188244290,49266375442110,
%U A377261 511157395433610,5287689996408612,54555878321808435,561579617798527185,5768783256563735265,59149668761521664040,605472238745163334116
%N A377261 Expansion of 1/(1 - 9*x*(1 + x))^(5/3).
%F A377261 a(n) = 3*((3*n+2)*a(n-1) + (3*n+4)*a(n-2))/n for n > 1.
%F A377261 a(n) = Sum_{k=0..n} (-9)^k * binomial(-5/3,k) * binomial(k,n-k).
%F A377261 a(n) ~ Gamma(1/3) * n^(2/3) * 3^(n + 3/2) * (3 + sqrt(13))^(n + 5/3) / (Pi * 13^(5/6) * 2^(n + 11/3)). - _Vaclav Kotesovec_, May 03 2025
%o A377261 (PARI) a(n) = sum(k=0, n, (-9)^k*binomial(-5/3, k)*binomial(k, n-k));
%Y A377261 Cf. A180400, A376568, A377260.
%Y A377261 Cf. A377235.
%K A377261 nonn
%O A377261 0,2
%A A377261 _Seiichi Manyama_, Oct 21 2024