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 A383313 #12 Apr 23 2025 05:42:22
%S A383313 1,0,1,4,27,232,2455,30852,449113,7432624,137829249,2830911220,
%T A383313 63796168579,1565078980536,41521403685463,1184510408920468,
%U A383313 36158133322895985,1176012432875399008,40599110984252798017,1482736219224857910756,57115359439245403771051
%N A383313 Expansion of e.g.f. exp(-x/2) / (1-2*x)^(1/4).
%F A383313 a(n) = (-1)^n * n! * Sum_{k=0..n} (1/2)^(n-2*k) * binomial(-1/4,k)/(n-k)!.
%F A383313 a(n) = (n-1) * (2*a(n-1) + a(n-2)) for n > 1.
%F A383313 a(n) ~ sqrt(Pi) * 2^(n + 1/2) * n^(n - 1/4) / (Gamma(1/4) * exp(n + 1/4)). - _Vaclav Kotesovec_, Apr 23 2025
%o A383313 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x/2)/(1-2*x)^(1/4)))
%Y A383313 Cf. A383314, A383315.
%Y A383313 Cf. A002801.
%K A383313 nonn
%O A383313 0,4
%A A383313 _Seiichi Manyama_, Apr 23 2025