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 A322262 #25 Mar 29 2023 15:25:10
%S A322262 1,1,1,1,1,1,2,14,98,546,2562,10626,41118,174174,1093092,10005996,
%T A322262 98041944,889104216,7315812504,55893493656,421564046904,3519008733240,
%U A322262 36011379484080,435775334314320,5538098453968080,68428271204813520,805379194188288720
%N A322262 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 6).
%H A322262 Seiichi Manyama, <a href="/A322262/b322262.txt">Table of n, a(n) for n = 0..514</a>
%H A322262 David Galvin, John Engbers, and Clifford Smyth, <a href="https://arxiv.org/abs/2303.14057">Reciprocals of thinned exponential series</a>, arXiv:2303.14057 [math.CO], 2023.
%H A322262 Ira M. Gessel, <a href="https://arxiv.org/abs/1807.09290">Reciprocals of exponential polynomials and permutation enumeration</a>, arXiv:1807.09290 [math.CO], 2018.
%F A322262 E.g.f.: 1/(1 - x + x^2/2! - x^3/3! + x^4/4! - x^5/5!).
%e A322262 For n=6 the a(6)=2 permutations are 654321 and 123456.
%o A322262 (PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/sum(k=0, 5, (-x)^k/k!)))
%Y A322262 Cf. A000142, A322251 (mod 3), A317111 (mod 4), A322276 (mod 5).
%K A322262 nonn
%O A322262 0,7
%A A322262 _Seiichi Manyama_, Dec 01 2018