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 A377233 #15 May 04 2025 04:24:25
%S A377233 1,6,51,456,4191,39174,370329,3529284,33838854,325978044,3152058630,
%T A377233 30572797920,297294956070,2897207397420,28286321963370,
%U A377233 276611636831640,2708781551458665,26559205696513590,260695647288540915,2561413004129212440,25188928968792165495
%N A377233 Expansion of 1/(1 - 9*x/(1-x))^(2/3).
%F A377233 a(0) = 1; a(n) = 3 * Sum_{k=0..n-1} (2+k/n) * a(k).
%F A377233 a(n) = ((11*n-5)*a(n-1) - 10*(n-2)*a(n-2))/n for n > 1.
%F A377233 a(n) = Sum_{k=0..n} (-9)^k * binomial(-2/3,k) * binomial(n-1,n-k).
%F A377233 a(n) ~ Gamma(1/3) * 3^(11/6) * 2^(n - 5/3) * 5^(n - 2/3) / (Pi * n^(1/3)). - _Vaclav Kotesovec_, Oct 21 2024
%F A377233 a(n) = 6*hypergeom([5/3, 1-n], [2], -9) for n > 0. - _Stefano Spezia_, May 04 2025
%o A377233 (PARI) a(n) = sum(k=0, n, (-9)^k*binomial(-2/3, k)*binomial(n-1, n-k));
%Y A377233 Cf. A052268, A361375, A377234, A377235.
%K A377233 nonn
%O A377233 0,2
%A A377233 _Seiichi Manyama_, Oct 21 2024