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 A276837 #16 May 09 2019 18:27:15 %S A276837 1,1,0,1,1,0,1,1,1,0,1,1,2,1,0,1,1,2,3,1,0,1,1,2,6,5,1,0,1,1,2,6,12,8, %T A276837 1,0,1,1,2,6,24,25,13,1,0,1,1,2,6,24,60,57,21,1,0,1,1,2,6,24,120,150, %U A276837 124,34,1,0,1,1,2,6,24,120,360,399,268,55,1,0 %N A276837 Number A(n,k) of permutations of [n] such that for each cycle c the smallest integer interval containing all elements of c has at most k elements; square array A(n,k), n>=0, k>=0, read by antidiagonals. %C A276837 The sequence of column k satisfies a linear recurrence with constant coefficients of order 2^(k-1) for k>0. %H A276837 Alois P. Heinz, <a href="/A276837/b276837.txt">Antidiagonals n = 0..30, flattened</a> %H A276837 Alice L. L. Gao, Sergey Kitaev, <a href="https://arxiv.org/abs/1903.08946">On partially ordered patterns of length 4 and 5 in permutations</a>, arXiv:1903.08946 [math.CO], 2019 %F A276837 A(n,k+1) - A(n,k) = A263757(n,k) for n>0. %e A276837 Square array A(n,k) begins: %e A276837 1, 1, 1, 1, 1, 1, 1, 1, 1, ... %e A276837 0, 1, 1, 1, 1, 1, 1, 1, 1, ... %e A276837 0, 1, 2, 2, 2, 2, 2, 2, 2, ... %e A276837 0, 1, 3, 6, 6, 6, 6, 6, 6, ... %e A276837 0, 1, 5, 12, 24, 24, 24, 24, 24, ... %e A276837 0, 1, 8, 25, 60, 120, 120, 120, 120, ... %e A276837 0, 1, 13, 57, 150, 360, 720, 720, 720, ... %e A276837 0, 1, 21, 124, 399, 1050, 2520, 5040, 5040, ... %e A276837 0, 1, 34, 268, 1145, 3192, 8400, 20160, 40320, ... %Y A276837 Columns k=0-10 give: A000007, A000012, A000045(n+1), A214663, A276838, A276839, A276840, A276841, A276842, A276843, A276844. %Y A276837 Main diagonal gives A000142. %Y A276837 Cf. A263757, A276719. %K A276837 nonn,tabl %O A276837 0,13 %A A276837 _Alois P. Heinz_, Sep 20 2016