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 A383315 #12 Apr 23 2025 10:34:33
%S A383315 1,0,3,36,675,16632,509085,18626436,793001097,38511087120,
%T A383315 2101009734099,127215916659540,8465583820754907,614101808094096744,
%U A383315 48230098800348987405,4077120575169267005268,369111206211249734907345,35630377583888099367357984,3653123185073359871950788963
%N A383315 Expansion of e.g.f. exp(-x/2) / (1-6*x)^(1/12).
%F A383315 a(n) = (-1)^n * n! * Sum_{k=0..n} 3^k * (1/2)^(n-2*k) * binomial(-1/12,k)/(n-k)!.
%F A383315 a(n) = 3*(n-1) * (2*a(n-1) + a(n-2)) for n > 1.
%F A383315 a(n) ~ Pi * (2 - sqrt(3))^(1/4) * 2^(n + 1/2) * 3^(n - 3/8) * n^(n - 5/12) / (Gamma(1/3) * Gamma(1/4) * exp(n + 1/12)). - _Vaclav Kotesovec_, Apr 23 2025
%o A383315 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-x/2)/(1-6*x)^(1/12)))
%Y A383315 Cf. A383313, A383314.
%K A383315 nonn
%O A383315 0,3
%A A383315 _Seiichi Manyama_, Apr 23 2025