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 A386861 #29 Aug 20 2025 03:11:19
%S A386861 0,0,6,150,3240,72030,1720320,44641044,1260000000,38584598580,
%T A386861 1277045637120,45493302310170,1737263457785856,70841500488281250,
%U A386861 3073706745680363520,141437374309896780360,6881573428807007600640,353052290206768309241544,19051315200000000000000000
%N A386861 The total number of big inversions in all parking functions of length n.
%C A386861 A big inversion in a parking function (x_1,x_2,...,x_k) is a pair of integers i,j in [k] with i < j such that x_i - x_{j} >= 2.
%H A386861 Amanda Priestley, <a href="/A386861/b386861.txt">Table of n, a(n) for n = 1..100</a>
%H A386861 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.
%F A386861 a(n) = (n/4)*(n-1)*(n-2)*(n+1)^(n-2).
%F A386861 a(n) = A386860(n)*n/2. - _Paolo Xausa_, Aug 07 2025
%e A386861 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.
%e A386861 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.
%t A386861 a[n_]:=(n/4)*(n-1)*(n-2)*(n+1)^(n-2); Array[a,19] (* _Stefano Spezia_, Aug 06 2025 *)
%Y A386861 Cf. A000272(n+1) (parking functions), A386860.
%K A386861 nonn,easy
%O A386861 1,3
%A A386861 _Amanda Priestley_, Aug 05 2025