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 A057546 #16 Jan 11 2024 13:26:32
%S A057546 1,1,2,3,5,6,10,11,18,21,34,35,68,69,137,148,316,317,759,760,1869,
%T A057546 1915,4833,4834,12796,12802,34108,34384,92792,92793,254752,254753,
%U A057546 703083,704956,1958210,1958231,5485330,5485331,15427026,15440591,43618394,43618395,123807695,123807696,352561832,352664217,1007481494,1007481495,2887387009
%N A057546 Number of Catalan objects of size n fixed by Catalan Automorphism A057511/A057512 (deep rotation of general parenthesizations/plane trees).
%C A057546 Greater than A003238 because there exists also parenthesizations like ((() (())) ((()) ())) and (((()) ()) (() (()))) which are fixed by recursive deep rotation, corresponding to Catalan mountain ranges below:
%C A057546 ...../\..../\............................./\......../\
%C A057546 ../\/__\../__\/\.....and.its."dual"....../__\/\../\/__\
%C A057546 ./______\/______\......................./______\/______\
%C A057546 It's obvious that a(p) = a(p-1)+1 for all primes p.
%H A057546 <a href="/index/Par#parens">Index entries for sequences related to parenthesizing</a>
%F A057546 a(0)=1, a(n) = A079216(n, 1) = Sum_{d|n} A079216(d-1, n/d). - _Antti Karttunen_, Jan 03 2003
%p A057546 with(numtheory,divisors); A057546 := proc(n) local d; if(0=n) then RETURN(1); else RETURN(add(A079216bi(d-1,n/d),d=divisors(n))); fi; end;
%Y A057546 The first row of A079216. The leftmost edge of the triangle A079217 and also its row sums shifted by one. Occurs for first time in A073202 as row 12. Cf. A057513, A079223-A079227, A034731, A003238.
%K A057546 nonn
%O A057546 0,3
%A A057546 _Antti Karttunen_, Sep 07 2000