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A342860 Irregular table read by rows: T(n,k) is the number of permutations in S_n that have exactly k occurrences of the pattern 2413. 0 <= k <= A342854(n).

%I A342860 #22 Mar 28 2021 07:05:40
%S A342860 1,1,2,6,23,1,103,9,8,512,62,82,34,28,2,2740,402,612,384,466,94,232,
%T A342860 42,60,8,15485,2593,4187,3036,4356,1746,3132,1064,1918,909,654,333,
%U A342860 612,144,104,22,24,1,91245,16921,28065,21638,33274,17598,31180,12942,24000,14290,15434,7770,15692,5965,6896,3947,5660,2226,3674,1314,1512,516,508,204,332,37,40
%N A342860 Irregular table read by rows: T(n,k) is the number of permutations in S_n that have exactly k occurrences of the pattern 2413. 0 <= k <= A342854(n).
%C A342860 Equivalently the table for the pattern 3142.
%C A342860 First column is A022558.
%H A342860 Peter Kagey, <a href="/A342860/b342860.txt">Rows n = 0..13, flattened</a>, based on Anders Kaseorg's Rust program in the Code Golf Stack Exchange link.
%H A342860 Anders Kaseorg, <a href="https://codegolf.stackexchange.com/a/222494/53884">Answer: Patterns in Permutations</a>, Code Golf Stack Exchange.
%e A342860 Triangle begins:
%e A342860   n\k|       0       1        2        3        4        5        6
%e A342860   ---+------------------------------------------------------------------
%e A342860    0 |       1;
%e A342860    1 |       1;
%e A342860    2 |       2;
%e A342860    3 |       6;
%e A342860    4 |      23,      1;
%e A342860    5 |     103,      9,       8;
%e A342860    6 |     512,     62,      82,      34,      28,       2;
%e A342860    7 |    2740,    402,     612,     384,     466,      94,     232, ...
%e A342860    8 |   15485,   2593,    4187,    3036,    4356,    1746,    3132, ...
%e A342860    9 |   91245,  16921,   28065,   21638,   33274,   17598,   31180, ...
%e A342860   10 |  555662, 112196,  188514,  149946,  237128,  140954,  257686, ...
%e A342860   11 | 3475090, 755920, 1278590, 1036826, 1658064, 1041598, 1933438, ...
%Y A342860 Cf. A022558, A342854.
%Y A342860 Analogous for other patterns: A008302 (12), A138159 (321), A263771 (312), A342840 (1342), A342861 (1324), A342862 (2143), A342863 (1243), A342864 (1432), A342865 (1234).
%K A342860 nonn,tabf
%O A342860 0,3
%A A342860 _Peter Kagey_, Mar 26 2021