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 A342865 #19 Mar 28 2021 04:05:57 %S A342865 1,1,2,6,23,1,103,12,4,0,0,1,513,102,63,10,6,12,8,0,0,5,0,0,0,0,0,1, %T A342865 2761,770,665,196,146,116,142,46,10,72,32,24,0,13,0,12,18,0,0,10,0,0, %U A342865 0,0,0,6,0,0,0,0,0,0,0,0,0,1 %N A342865 Irregular table read by rows: T(n,k) is the number of permutations in S_n that have exactly k occurrences of the pattern 1234. 0 <= k <= A000332(n). %C A342865 Equivalently the table for the pattern 4321. %C A342865 First column is A005802. %H A342865 Peter Kagey, <a href="/A342865/b342865.txt">Rows n = 0..13, flattened</a>, based on Anders Kaseorg's Rust program in the Code Golf Stack Exchange link. %H A342865 Anders Kaseorg, <a href="https://codegolf.stackexchange.com/a/222494/53884">Answer: Patterns in Permutations</a>, Code Golf Stack Exchange. %e A342865 Table begins: %e A342865 n\k| 0 1 2 3 4 5 6 %e A342865 ---+------------------------------------------------------------------- %e A342865 0 | 1; %e A342865 1 | 1; %e A342865 2 | 2; %e A342865 3 | 6; %e A342865 4 | 23, 1; %e A342865 5 | 103, 12, 4, 0, 0, 1; %e A342865 6 | 513, 102, 63, 10, 6, 12, 8, ... %e A342865 7 | 2761, 770, 665, 196, 146, 116, 142, ... %e A342865 8 | 15767, 5545, 5982, 2477, 2148, 1204, 1782, ... %e A342865 9 | 94359, 39220, 49748, 25886, 25190, 13188, 19936, ... %e A342865 10 | 586590, 276144, 396642, 244233, 260505, 142550, 210663, ... %e A342865 11 | 3763290, 1948212, 3089010, 2167834, 2493489, 1476655, 2136586, ... %Y A342865 Cf. A000332, A005802. %Y A342865 Analogous for other patterns: A008302 (12), A138159 (321), A263771 (312), A342840 (1342), A342860 (2413), A342861 (1324), A342862 (2143), A342863 (1243), A342864 (1432). %K A342865 nonn,tabf %O A342865 0,3 %A A342865 _Peter Kagey_, Mar 26 2021