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 A322282 #23 Mar 29 2023 15:25:27
%S A322282 1,1,1,1,1,1,1,1,2,18,162,1122,6402,31746,141570,580866,2241096,
%T A322282 8693256,43232904,362491272,4067218584,45304757784,459941563224,
%U A322282 4236342378840,35804034476496,281634733757520,2106753678778320,15739783039815120
%N A322282 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 8).
%H A322282 Seiichi Manyama, <a href="/A322282/b322282.txt">Table of n, a(n) for n = 0..537</a>
%H A322282 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 A322282 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 A322282 E.g.f.: 1/(1 - x + x^2/2! - x^3/3! + x^4/4! - x^5/5! + x^6/6! - x^7/7!).
%t A322282 m = 28; CoefficientList[1/Normal[Exp[-x]+O[x]^8]+O[x]^m, x]*Range[0, m-1]! (* _Jean-François Alcover_, Feb 24 2019 *)
%o A322282 (PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/sum(k=0, 7, (-x)^k/k!)))
%Y A322282 Cf. A000142, A322251 (mod 3), A317111 (mod 4), A322276 (mod 5), A322262 (mod 6), A322297 (mod 7), A322298 (mod 9), A322283 (mod 10).
%K A322282 nonn
%O A322282 0,9
%A A322282 _Seiichi Manyama_, Dec 02 2018