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 A370570 #9 Feb 22 2024 10:42:02
%S A370570 1,1,1,3,17,95,594,4280,35018,320636,3249951,36140133,437572800,
%T A370570 5731086422,80745062993,1217782176949,19576722067015,334183547442139,
%U A370570 6037316140379389,115082343658784617,2308352556410956084,48602560660569621128,1071794851776260190000
%N A370570 Number of permutations of [n] having no adjacent 2-cycles and no adjacent 3-cycles.
%F A370570 G.f.: Sum_{k>=0} k! * x^k / (1+x^2+x^3)^(k+1).
%F A370570 a(n) = Sum_{i, j>=0 and 2*i+3*j<=n} (-1)^(i+j) * (n-i-2*j)!/(i!*j!).
%o A370570 (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 A370570 Cf. A370569.
%K A370570 nonn
%O A370570 0,4
%A A370570 _Seiichi Manyama_, Feb 22 2024