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 A057546 Number of Catalan objects of size n fixed by Catalan Automorphism A057511/A057512 (deep rotation of general parenthesizations/plane trees). 20
 1, 1, 2, 3, 5, 6, 10, 11, 18, 21, 34, 35, 68, 69, 137, 148, 316, 317, 759, 760, 1869, 1915, 4833, 4834, 12796, 12802, 34108, 34384, 92792, 92793, 254752, 254753, 703083, 704956, 1958210, 1958231, 5485330, 5485331, 15427026, 15440591, 43618394, 43618395, 123807695, 123807696, 352561832, 352664217, 1007481494, 1007481495, 2887387009 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Greater than A003238 because there exists also parenthesizations like ((() (())) ((()) ())) and (((()) ()) (() (()))) which are fixed by recursive deep rotation, corresponding to Catalan mountain ranges below: ...../\..../\............................./\......../\ ../\/__\../__\/\.....and.its."dual"....../__\/\../\/__\ ./______\/______\......................./______\/______\ It's obvious that a(p) = a(p-1)+1 for all primes p. LINKS FORMULA a(0)=1, a(n) = A079216(n, 1) = Sum_{d|n} A079216(d-1, n/d) MAPLE 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; CROSSREFS 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. Sequence in context: A000039 A302600 A053436 * A138587 A099350 A306296 Adjacent sequences:  A057543 A057544 A057545 * A057547 A057548 A057549 KEYWORD nonn AUTHOR Antti Karttunen Sep 07 2000. Formula added Jan 03 2003. STATUS approved

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Last modified January 19 03:54 EST 2020. Contains 331031 sequences. (Running on oeis4.)