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 A333310 #17 Mar 15 2020 02:48:45 %S A333310 1,0,1,0,1,1,0,1,1,1,0,1,2,1,2,0,1,2,2,1,3,0,1,3,5,2,3,5,0,1,3,6,5,3, %T A333310 4,8,0,1,4,8,12,8,5,9,13,0,1,4,12,20,18,8,11,13,21,0,1,5,18,29,42,21, %U A333310 22,19,27,38,0,1,5,23,44,69,48,33,30,33,38,64 %N A333310 Triangle read by rows: T(n,k) is the number of permutations sigma of [n] such that sigma(1) = k and sigma(j)/j > sigma(j+1)/(j+1) for 1 <= j <= n-1. %C A333310 T(n+1,k+1) is equal to the number of permutations sigma of [n] such that sigma(1) = k and sigma(j)/j >= sigma(j+1)/(j+1) for 1 <= j <= n-1. %H A333310 Seiichi Manyama, <a href="/A333310/b333310.txt">Rows n = 1..18, flattened</a> %H A333310 Mathematics.StackExchange, <a href="https://math.stackexchange.com/questions/3572301/why-are-the-numbers-of-two-different-permutations-the-same">Why are the numbers of two different permutations the same?</a>, Mar 07 2020. %e A333310 Triangle begins: %e A333310 n\k | 1 2 3 4 5 6 7 8 9 10 11 12 %e A333310 -----+-------------------------------------------- %e A333310 1 | 1; %e A333310 2 | 0, 1; %e A333310 3 | 0, 1, 1; %e A333310 4 | 0, 1, 1, 1; %e A333310 5 | 0, 1, 2, 1, 2; %e A333310 6 | 0, 1, 2, 2, 1, 3; %e A333310 7 | 0, 1, 3, 5, 2, 3, 5; %e A333310 8 | 0, 1, 3, 6, 5, 3, 4, 8; %e A333310 9 | 0, 1, 4, 8, 12, 8, 5, 9, 13; %e A333310 10 | 0, 1, 4, 12, 20, 18, 8, 11, 13, 21; %e A333310 11 | 0, 1, 5, 18, 29, 42, 21, 22, 19, 27, 38; %e A333310 12 | 0, 1, 5, 23, 44, 69, 48, 33, 30, 33, 38, 64; %Y A333310 Row sums give A309807. %Y A333310 Cf. A332954. %K A333310 nonn,tabl %O A333310 1,13 %A A333310 _Seiichi Manyama_, Mar 14 2020