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 A342140 #43 Apr 24 2021 10:31:22 %S A342140 1,1,3,2,17,4,86,4,488,12,3172,40,22912,56,166814,256 %N A342140 Number of permutations of degree n with greatest sum of distances and highest Shannon entropy. %C A342140 Starting from a list of n ordered numbers, the sequence gives the number of permutations of the list that display both the greatest sum of distances (see A007590 and A062870) and the highest Shannon entropy (see A341838 for a more in-depth explanation on how to calculate it). %C A342140 A way to interpret this is to see these permutations as the ones with both the highest level of disorder and the greatest distance from a starting configuration. %H A342140 Andrea G. Amato <a href="https://medium.com/@andrea.g.amato/how-well-can-you-shuffle-a-deck-of-cards-31f9f9c87de1">How well can you shuffle a deck of cards?</a> %H A342140 Andrea G. Amato, <a href="/A342140/a342140.txt">Conjectures and properties</a> %e A342140 Starting from (1,2,3,4), there are only two permutations that have both the greatest sum of distances (which is 8 for n=4) and the highest Shannon entropy (which is 1.039720... for n=4). These permutations are (3,4,2,1) and (4,3,1,2). %Y A342140 Cf. A007590 (greatest sum of distances of a given n). %Y A342140 Cf. A062870 (permutations that possess this property). %Y A342140 Cf. A341838 (number of permutations with the highest Shannon entropy). %K A342140 nonn,hard,more %O A342140 1,3 %A A342140 _Andrea G. Amato_, Mar 01 2021 %E A342140 a(13)-a(15) from _Hugo Pfoertner_, Mar 02 2021 %E A342140 a(16) from _Hugo Pfoertner_, Mar 07 2021