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 A370525 #18 Feb 24 2024 10:24:23
%S A370525 0,0,0,1,2,6,22,114,696,4923,39612,357900,3588836,39556420,475392840,
%T A370525 6187284605,86701097310,1301467245330,20835850494474,354382860600678,
%U A370525 6381494425302864,121290065781743383,2426510081356069016,50969474697328055064,1121571023472780698152
%N A370525 Number of permutations of [n] having exactly one adjacent 3-cycle.
%H A370525 R. A. Brualdi and Emeric Deutsch, <a href="http://arxiv.org/abs/1005.0781">Adjacent q-cycles in permutations</a>, arXiv:1005.0781 [math.CO], 2010.
%F A370525 G.f.: Sum_{k>=1} k! * x^(k+2) / (1+x^3)^(k+1).
%F A370525 a(n) = Sum_{k=0..floor(n/3)-1} (-1)^k * (n-2*k-2)! / k!.
%o A370525 (PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, N, k!*x^(k+2)/(1+x^3)^(k+1))))
%o A370525 (PARI) a(n, k=1, q=3) = sum(j=0, n\q-k, (-1)^j*(n-(q-1)*(j+k))!/j!)/k!;
%Y A370525 Column k=3 of A370527.
%Y A370525 Column k=1 of A177250.
%Y A370525 Cf. A177251, A370528, A370530.
%K A370525 nonn
%O A370525 0,5
%A A370525 _Seiichi Manyama_, Feb 21 2024