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 A383317 #14 Apr 23 2025 05:47:27
%S A383317 1,1,4,46,838,20398,619768,22564252,957247708,46363595644,
%T A383317 2524152072304,152582368541224,10139721673875976,734706716925462184,
%U A383317 57646381491830349472,4869084744694710293392,440492624600086270972432,42494068518463022190243088,4354423933547086885775444032
%N A383317 Expansion of e.g.f. exp(x/2) / (1-6*x)^(1/12).
%F A383317 a(n) = n! * Sum_{k=0..n} (-3)^k * (1/2)^(n-2*k) * binomial(-1/12,k)/(n-k)!.
%F A383317 a(n) = (6*n-5)*a(n-1) - 3*(n-1)*a(n-2) for n > 1.
%F A383317 From _Vaclav Kotesovec_, Apr 23 2025: (Start)
%F A383317 a(n) ~ (sqrt(3) - 1) * 2^(n-1) * 3^n * n^(n - 5/12) * Gamma(11/12) / (sqrt(Pi) * exp(n - 1/12)).
%F A383317 Equivalently, 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)). (End)
%o A383317 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/2)/(1-6*x)^(1/12)))
%Y A383317 Cf. A002801, A383316.
%K A383317 nonn
%O A383317 0,3
%A A383317 _Seiichi Manyama_, Apr 23 2025