A342270 Irregular triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n!) = number of permutations on n letters whose fiber under the parking function map phi has size k.

1, 1, 1, 1, 3, 1, 0, 0, 1, 1, 6, 4, 4, 0, 4, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 10, 10, 20, 1, 20, 0, 15, 0, 6, 0, 15, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 5, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1,5

Links

Table of n, a(n) for n=1..153.

Laura Colmenarejo, Pamela E. Harris, Zakiya Jones, Christo Keller, Andrees Ramos Rodriguez Eunice Sukarto and Andres R. Vindas-Melendez, Counting k-Naples Parking Functions Through Permutations and the k-Naples Area Statistic, Enumerative Combinatorics and Applications, ECA 1:2 (2021) Article S2R11. See page 9. Proposition 4.1 gives a recurrence.

Example

Triangle begins:
1,
1,1,
1,3,1,0,0,1,
1,6,4,4,0,4,0,3,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,
...
Row 3 is 1,3,1,0,0,1 as F3(q) = q + 3q^2 + q^3 + q^6 = q + 3q^2 + q^3 + 0q^4 + 0 q^5 + q^6. k in name are exponents in the power q^k and terms in rows are coefficients. The row lists the coefficients starting at k = 1 and ending at k = n!. - David A. Corneth, Mar 07 2021

Crossrefs

Sequence in context: A205531 A269246 A334566 * A330248 A247505 A117389

Adjacent sequences: A342267 A342268 A342269 * A342271 A342272 A342273

Keyword

nonn,tabf

Author

N. J. A. Sloane, Mar 07 2021

Status

approved