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 A358525 #6 Nov 21 2022 22:01:49
%S A358525 1,1,1,1,1,2,2,1,1,2,1,3,2,3,3,1,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,1,1,2,
%T A358525 2,3,1,6,6,4,2,6,1,6,6,6,6,5,2,3,6,4,6,6,6,5,3,4,6,5,4,5,5,1,1,2,2,3,
%U A358525 2,6,6,4,2,3,3,12,3,12,12,5,2,6,3,12,3,4
%N A358525 Number of distinct permutations of the n-th composition in standard order.
%C A358525 The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.
%H A358525 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vTCPiJVFUXN8IqfLlCXkgP15yrGWeRhFS4ozST5oA4Bl2PYS-XTA3sGsAEXvwW-B0ealpD8qnoxFqN3/pub">Statistics, classes, and transformations of standard compositions</a>
%e A358525 The a(45) = 6 permutations are: (2121), (2112), (2211), (1221), (1212), (1122).
%t A358525 stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
%t A358525 Table[Length[Permutations[stc[n]]],{n,0,100}]
%Y A358525 See link for sequences related to standard compositions.
%Y A358525 Positions of 1's are A272919.
%Y A358525 Cf. A000120, A048896, A070939, A329395, A333766, A358371, A358372, A358379, A358505, A358507, A358508.
%K A358525 nonn
%O A358525 0,6
%A A358525 _Gus Wiseman_, Nov 21 2022