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 A373538 #11 Jun 10 2024 10:02:21
%S A373538 1,1,1,-5,-23,61,961,-209,-64175,-197063,6153121,48453571,-775290119,
%T A373538 -12038136395,116706067297,3475641927031,-17614393396319,
%U A373538 -1188106176788879,782498662651585,478042340115562507,1987706898622853641,-223468834844001403859
%N A373538 Expansion of e.g.f. exp(x/(1 + x^2)).
%F A373538 a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * binomial(n-k-1,k)/(n-2*k)!.
%F A373538 a(n) == 1 mod 6.
%o A373538 (PARI) a(n) = n!*sum(k=0, n\2, (-1)^k*binomial(n-k-1, k)/(n-2*k)!);
%Y A373538 Cf. A012019.
%K A373538 sign
%O A373538 0,4
%A A373538 _Seiichi Manyama_, Jun 09 2024