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%I #9 Feb 22 2024 10:42:02
%S 1,1,1,3,17,95,594,4280,35018,320636,3249951,36140133,437572800,
%T 5731086422,80745062993,1217782176949,19576722067015,334183547442139,
%U 6037316140379389,115082343658784617,2308352556410956084,48602560660569621128,1071794851776260190000
%N Number of permutations of [n] having no adjacent 2-cycles and no adjacent 3-cycles.
%F G.f.: Sum_{k>=0} k! * x^k / (1+x^2+x^3)^(k+1).
%F a(n) = Sum_{i, j>=0 and 2*i+3*j<=n} (-1)^(i+j) * (n-i-2*j)!/(i!*j!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k/(1+x^2+x^3)^(k+1)))
%Y Cf. A370569.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Feb 22 2024