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 A387062 #20 Aug 17 2025 01:38:21
%S A387062 1,1,2,5,14,51,176,807,3232,17449,78384,479897,2366248,16041147,
%T A387062 85534176,631596455,3602770400,28633529345,173300710720,1469070416505,
%U A387062 9373542317760,84152568224563,563142033172480,5323835899152567,37206559614499840,368667413713034441,2681213937595142656
%N A387062 a(n) = number of wiggly permutations |W_n|.
%C A387062 Permutation P over [n] is said to be wiggly given the following two items hold for all pairs of values of the form (2*j-1, 2*j):
%C A387062 For upward order: if 2*j-1 appears before 2*j in P, then interposing terms are larger.
%C A387062 For downward order: if 2*j occurs before 2*j-1 in P, then interposing terms are smaller.
%H A387062 Vincent Pilaud and Aaron Williams, <a href="https://www.researchgate.net/publication/394425368_Skipping_Ropes_An_Efficient_Gray_Code_Algorithm_for_Generating_Wiggly_Permutations">Skipping Ropes: An Efficient Gray Code Algorithm for Generating Wiggly Permutations</a>, Conf. Algor. Data Struct. Symp. (WADS 2025). See pp. 6-7.
%e A387062 W_2 = {12, 21},
%e A387062 W_3 = {123, 132, 213, 312, 321},
%e A387062 W_4 = {1234, 1243, 1342, 1423, 1432, 2134, 2143, 3412, 3421, 4123, 4132, 4213, 4312, 4321}.
%Y A387062 Cf. A344654.
%K A387062 nonn
%O A387062 0,3
%A A387062 _Michael De Vlieger_, Aug 15 2025
%E A387062 a(17)-a(26) from _Alois P. Heinz_, Aug 17 2025