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).

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, 2761, 770, 665, 196, 146, 116, 142, 46, 10, 72, 32, 24, 0, 13, 0, 12, 18, 0, 0, 10, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset: 0

Author

Peter Kagey, Mar 26 2021

Keywords

• nonn
• tabf

Comments

Equivalently the table for the pattern 4321.

First column is A005802.

Examples

			Table begins:
  n\k|       0        1        2        3        4        5        6
  ---+-------------------------------------------------------------------
   0 |       1;
   1 |       1;
   2 |       2;
   3 |       6;
   4 |      23,       1;
   5 |     103,      12,       4,       0,       0,       1;
   6 |     513,     102,      63,      10,       6,      12,       8, ...
   7 |    2761,     770,     665,     196,     146,     116,     142, ...
   8 |   15767,    5545,    5982,    2477,    2148,    1204,    1782, ...
   9 |   94359,   39220,   49748,   25886,   25190,   13188,   19936, ...
  10 |  586590,  276144,  396642,  244233,  260505,  142550,  210663, ...
  11 | 3763290, 1948212, 3089010, 2167834, 2493489, 1476655, 2136586, ...
		

Links

• Peter Kagey, Rows n = 0..13, flattened, based on Anders Kaseorg's Rust program in the Code Golf Stack Exchange link.
• Anders Kaseorg, Answer: Patterns in Permutations, Code Golf Stack Exchange.

Crossrefs

Cf. A000332, A005802.

Analogous for other patterns: A008302 (12), A138159 (321), A263771 (312), A342840 (1342), A342860 (2413), A342861 (1324), A342862 (2143), A342863 (1243), A342864 (1432).