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 A370323 #20 Feb 22 2024 10:41:58
%S A370323 1,0,0,1,6,35,217,1568,12848,117738,1194019,13282346,160856190,
%T A370323 2107154067,29691159876,447836111629,7199765822643,122909558878512,
%U A370323 2220556571338744,42329227454294820,849072524072460101,17877662074795269964,394248958294191005180
%N A370323 Number of derangements of [n] having no adjacent 2-cycles, no adjacent 3-cycles and no adjacent 4-cycles.
%F A370323 G.f.: Sum_{k>=0} k! * x^k * ( (1-x)/(1-x^5) )^(k+1).
%F A370323 a(n) = Sum_{i, j, k, l>=0 and i+2*j+3*k+4*l<=n} (-1)^(i+j+k+l) * (n-j-2*k-3*l)!/(i!*j!*k!*l!).
%o A370323 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k*((1-x)/(1-x^5))^(k+1)))
%Y A370323 Cf. A000166, A177258, A177261, A370324.
%K A370323 nonn
%O A370323 0,5
%A A370323 _Seiichi Manyama_, Feb 22 2024