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 A372842 #30 Dec 27 2024 08:48:42 %S A372842 2,11,87,908,11824,184944,3381341,70805696,1671605646,43938023168, %T A372842 1272792377875,40291409169408,1383927524621468,51265193822056448, %U A372842 2037343816037147001,86467962304018300928,3903480077867017448410,186771397981175865606144,9441767566333191196904591 %N A372842 a(n) is the number of parking functions of order n for which the second spot is lucky. %C A372842 This sequence enumerates parking functions with lucky second spot (where a lucky spot is one which is parked in by a car which prefers that spot). %H A372842 Michael De Vlieger, <a href="/A372842/b372842.txt">Table of n, a(n) for n = 2..387</a> %H A372842 Steve Butler, Kimberly Hadaway, Victoria Lenius, Preston Martens, and Marshall Moats, <a href="https://arxiv.org/abs/2412.07873">Lucky cars and lucky spots in parking functions</a>, arXiv:2412.07873 [math.CO], 2024. See p. 10. %F A372842 a(n) = (3/4)*(n+1)^(n-1) - (1/4)*(n-1)^(n-1). %e A372842 For clarity, we write parentheses around parking functions. For n = 2, the a(2) = 2 solutions are the parking functions of length 2 with a lucky second spot are (1,2) and (2,1). The parking function (1,1) is not one of the solutions because the car which parks in the second spot did not prefer the second spot; this parking function does not contribute to our count. %t A372842 Array[(3/4)*(# + 1)^(# - 1) - (1/4)*(# - 1)^(# - 1) &, 19, 2] (* _Michael De Vlieger_, Jun 26 2024 *) %o A372842 (Python) %o A372842 def A372842(n): return 3*(n+1)**(n-1)-(n-1)**(n-1)>>2 # _Chai Wah Wu_, Jun 26 2024 %Y A372842 Cf. A000272 (for first spot), A372843 (for third spot), A372844 (for fourth spot), and A372845 (for fifth spot). %K A372842 nonn %O A372842 2,1 %A A372842 _Kimberly P. Hadaway_, Jun 20 2024