Amanda Priestley has authored 3 sequences.
A387047
Number of parking functions of size n with a big descent in the first position.
Original entry on oeis.org
0, 0, 2, 25, 324, 4802, 81920, 1594323, 35000000, 857435524, 23219011584, 689292459245, 22272608433152, 778478027343750, 29273397577908224, 1178644785915806503, 50599804623580938240, 2307531308540969341448, 111411200000000000000000, 5677927131570439768106049
Offset: 1
a(2)=0 because in the 3 parking functions of length 2 (11, 12, 21), there are 0 descents where the difference is strictly greater than one (and thus none in occur in the first position).
a(3)=2 because in the 16 parking functions of length 3, only 2 have a big descent occurring in the first position, 311 and 312.
a(4)=25 because in the 125 parking functions of length 4 there are 25 which have a big descent occurring in position 1. 3111, 4111, 3112, 3121, 4112, 4121, 4211, 3113, 3131, 3114, 3141, 4113, 4131, 3122, 4122, 4212, 4221, 3123, 3132, 3124, 3142, 4123, 4132, 4213, 4231.
- Amanda Priestley, Table of n, a(n) for n = 1..100
- Kyle Celano, Jennifer Elder, Kimberly P. Hadaway, Pamela E. Harris, Amanda Priestley, and Gabe Udell, Inversions in parking functions, arXiv:2508.11587 [math.CO], 2025.
A386860
The total number of big descents in all parking functions of length n.
Original entry on oeis.org
0, 0, 4, 75, 1296, 24010, 491520, 11160261, 280000000, 7716919716, 232190115840, 7582217051695, 267271301197824, 10120214355468750, 409827566090715136, 17679671788737097545, 809596873977295011840, 39228032245196478804616, 2005401600000000000000000, 107880615499838355594014931
Offset: 1
a(2) = 0 because in the 3 parking functions of length 2 (11, 12, 21), there are 0 descents where the difference is strictly greater than one.
a(3) = 4 as of the 16 parking functions of length 3 (111, 112, 122, 121, 212, 221, 211, 123, 132, 213, 312, 231, 321, 113, 131, 311) the parking functions (131, 311, 312, 231) all each have one big descent. Thus the total number of big descents in all parking functions of length 3 is 4.
- Amanda Priestley, Table of n, a(n) for n = 1..100
- Kyle Celano, Jennifer Elder, Kimberly P. Hadaway, Pamela E. Harris, Amanda Priestley, and Gabe Udell, Inversions in parking functions, arXiv:2508.11587 [math.CO], 2025.
A386861
The total number of big inversions in all parking functions of length n.
Original entry on oeis.org
0, 0, 6, 150, 3240, 72030, 1720320, 44641044, 1260000000, 38584598580, 1277045637120, 45493302310170, 1737263457785856, 70841500488281250, 3073706745680363520, 141437374309896780360, 6881573428807007600640, 353052290206768309241544, 19051315200000000000000000
Offset: 1
a(2) = 0 because in the 3 parking functions of length 2 (11, 12, 21), there are no inversions with difference strictly greater than one.
a(3) = 6 as in the 16 parking functions of length 3 (111, 112, 122, 121, 212, 221, 211, 123, 132, 213 312, 231, 321, 113, 131, 311) 312 has one big inversion, 231 has one, 321 has one, 131 has one, and 311 has 2. Thus, in the 16 parking functions of length 3 there are 6 total big inversions.
- Amanda Priestley, Table of n, a(n) for n = 1..100
- Kyle Celano, Jennifer Elder, Kimberly P. Hadaway, Pamela E. Harris, Amanda Priestley, and Gabe Udell, Inversions in parking functions, arXiv:2508.11587 [math.CO], 2025.
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