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 A381505 #13 Apr 23 2025 10:14:45
%S A381505 1,1,2,10,88,1064,16144,293968,6241280,151328512,4124855296,
%T A381505 124843943936,4153947277312,150699794606080,5919989155033088,
%U A381505 250339939417452544,11338037538551824384,547552961327680913408,28087260712728645468160,1525087432592278987866112
%N A381505 Expansion of e.g.f. exp(2*x/3) / (1-3*x)^(1/9).
%F A381505 a(n) = n! * Sum_{k=0..n} (-3)^k * (2/3)^(n-k) * binomial(-1/9,k)/(n-k)!.
%F A381505 a(n) = (3*n-2)*a(n-1) - 2*(n-1)*a(n-2) for n > 1.
%F A381505 a(n) ~ sqrt(2*Pi) * 3^n * n^(n - 7/18) / (Gamma(1/9) * exp(n - 2/9)). - _Vaclav Kotesovec_, Apr 23 2025
%o A381505 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(2*x/3)/(1-3*x)^(1/9)))
%Y A381505 Cf. A002801, A381506.
%K A381505 nonn
%O A381505 0,3
%A A381505 _Seiichi Manyama_, Apr 23 2025