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%I #8 Feb 22 2024 10:42:31
%S 1,1,1,4,18,97,607,4358,35523,324356,3280902,36427352,440515699,
%T 5764104507,81147821501,1223090709078,19651920713844,335323035157947,
%U 6055709997021397,115397482250691724,2314064310772997407,48711753977589111112,1073990818947724506060
%N Number of permutations of [n] having no adjacent 2-cycles and no adjacent 4-cycles.
%F G.f.: Sum_{k>=0} k! * x^k * ( (1-x^2)/(1-x^6) )^(k+1).
%F a(n) = Sum_{i, j>=0 and 2*i+4*j<=n} (-1)^(i+j) * (n-i-3*j)!/(i!*j!).
%o (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 Cf. A177251, A370324.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Feb 22 2024
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