A386011 Total number of inversions in all parking functions of length n.
0, 1, 18, 300, 5400, 108045, 2408448, 59521392, 1620000000, 48230748225, 1560833556480, 54591962772204, 2053129541019648, 82648417236328125, 3546584706554265600, 161642713497024891840, 7799116552647941947392, 397183826482614347896737
Offset: 1
Examples
a(2)=1 because in the 3 parking functions of length 2 (11, 12, 21), there is 1 inversion: (1,2).
Links
- Kyle Celano, 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.
- Richard P. Stanley, Parking Functions, 2011.
- Wikipedia, Parking function.
Programs
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Mathematica
Table[Binomial[n,2] * n*(n+1)^(n-2)/2, {n, 0, 18}]