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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.
0
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
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
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Mar 07 2021
STATUS
approved