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 A370569 #8 Feb 22 2024 10:42:31
%S A370569 1,1,1,4,18,97,607,4358,35523,324356,3280902,36427352,440515699,
%T A370569 5764104507,81147821501,1223090709078,19651920713844,335323035157947,
%U A370569 6055709997021397,115397482250691724,2314064310772997407,48711753977589111112,1073990818947724506060
%N A370569 Number of permutations of [n] having no adjacent 2-cycles and no adjacent 4-cycles.
%F A370569 G.f.: Sum_{k>=0} k! * x^k * ( (1-x^2)/(1-x^6) )^(k+1).
%F A370569 a(n) = Sum_{i, j>=0 and 2*i+4*j<=n} (-1)^(i+j) * (n-i-3*j)!/(i!*j!).
%o A370569 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k*((1-x^2)/(1-x^6))^(k+1)))
%Y A370569 Cf. A177251, A370324.
%K A370569 nonn
%O A370569 0,4
%A A370569 _Seiichi Manyama_, Feb 22 2024