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 A381484 #29 Apr 23 2025 10:19:45
%S A381484 1,0,1,6,57,708,10905,200538,4287633,104507496,2860291089,86853807630,
%T A381484 2897638853769,105357244427244,4146601837761513,175632278607964962,
%U A381484 7965651564924845985,385161391574120046672,19778647046883844762017,1074979845580061777989014
%N A381484 Expansion of e.g.f. exp(-x/3) / (1-3*x)^(1/9).
%F A381484 a(n) = (-1)^n * n! * Sum_{k=0..n} (1/3)^(n-2*k) * binomial(-1/9,k)/(n-k)!.
%F A381484 a(n) = (n-1) * (3*a(n-1) + a(n-2)) for n > 1.
%F A381484 a(n) ~ sqrt(2*Pi) * 3^n * n^(n - 7/18) / (Gamma(1/9) * exp(n + 1/9)). - _Vaclav Kotesovec_, Apr 23 2025
%o A381484 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-x/3)/(1-3*x)^(1/9)))
%Y A381484 Cf. A000166, A383313, A381504.
%K A381484 nonn
%O A381484 0,4
%A A381484 _Seiichi Manyama_, Apr 23 2025