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 A383316 #12 Apr 23 2025 10:29:22
%S A383316 1,1,3,23,281,4593,93643,2285959,64981809,2107824353,76819828499,
%T A383316 3107456481399,138145505435977,6694550810809297,351219409831557339,
%U A383316 19832058937696108007,1199219012904515868257,77314609952787255980481,5293934640303567123132451
%N A383316 Expansion of e.g.f. exp(x/2) / (1-4*x)^(1/8).
%F A383316 a(n) = n! * Sum_{k=0..n} (-2)^k * (1/2)^(n-2*k) * binomial(-1/8,k)/(n-k)!.
%F A383316 a(n) = (4*n-3)*a(n-1) - 2*(n-1)*a(n-2) for n > 1.
%F A383316 a(n) ~ sqrt(Pi) * 2^(2*n + 1/2) * n^(n - 3/8) / (Gamma(1/8) * exp(n - 1/8)). - _Vaclav Kotesovec_, Apr 23 2025
%o A383316 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/2)/(1-4*x)^(1/8)))
%Y A383316 Cf. A002801, A383317.
%K A383316 nonn
%O A383316 0,3
%A A383316 _Seiichi Manyama_, Apr 23 2025