This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A386011 #35 Aug 20 2025 10:43:55
%S A386011 0,1,18,300,5400,108045,2408448,59521392,1620000000,48230748225,
%T A386011 1560833556480,54591962772204,2053129541019648,82648417236328125,
%U A386011 3546584706554265600,161642713497024891840,7799116552647941947392,397183826482614347896737
%N A386011 Total number of inversions in all parking functions of length n.
%H A386011 Kyle Celano, <a href="/A386011/b386011.txt">Table of n, a(n) for n = 1..100</a>
%H A386011 Kyle Celano, Jennifer Elder, Kimberly P. Hadaway, Pamela E. Harris, Amanda Priestley, and Gabe Udell, <a href="https://arxiv.org/abs/2508.11587">Inversions in parking functions</a>, arXiv:2508.11587 [math.CO], 2025.
%H A386011 Richard P. Stanley, <a href="http://math.mit.edu/~rstan/transparencies/parking.pdf">Parking Functions</a>, 2011.
%H A386011 Wikipedia, <a href="https://en.wikipedia.org/wiki/Parking_function">Parking function</a>.
%F A386011 a(n) = binomial(n,2) * n*(n+1)^(n-2)/2.
%F A386011 a(n) = Sum_{k=0..binomial(n,2)} A152290(n,k)*k.
%F A386011 a(n) = binomial(n,2)*A055865(n)/2.
%e A386011 a(2)=1 because in the 3 parking functions of length 2 (11, 12, 21), there is 1 inversion: (1,2).
%t A386011 Table[Binomial[n,2] * n*(n+1)^(n-2)/2, {n, 0, 18}]
%Y A386011 Cf. A001809, A000272, A240796.
%K A386011 nonn,easy,changed
%O A386011 1,3
%A A386011 _Kyle Celano_, Jul 14 2025