

A057513


Number of separate orbits to which permutations given in A057511/A057512 (induced by deep rotation of general parenthesizations/plane trees) partition each A000108(n) objects encoded by A014486 between (A014138(n1)+1)th and (A014138(n))th terms.


13



1, 1, 2, 4, 9, 21, 56, 153, 451, 1357, 4212, 13308, 42898, 140276, 465324, 1561955, 5300285, 18156813, 62732842, 218405402, 765657940
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

It is much faster to compute this sequence empirically with the given Cprogram than to calculate the terms with the formula in its present form.


LINKS

Table of n, a(n) for n=0..20.
A. Karttunen, Gatomorphisms (with the complete Scheme source)
Index entries for sequences related to rooted trees
A. Karttunen, Cprogram for computing empirically the initial terms of this sequence


FORMULA

a(0)=1, a(n) = (1/A003418(n1))*Sum_{i=1..A003418(n1)} A079216(n, i) [Needs improvement.]


MAPLE

A057513 := proc(n) local i; `if`((0=n), 1, (1/A003418(n1))*add(A079216bi(n, i), i=1..A003418(n1))); end;
# Or empirically:
DeepRotatePermutationCycleCounts := proc(upto_n) local u, n, a, r, b; a := []; for n from 0 to upto_n do b := []; u := (binomial(2*n, n)/(n+1)); for r from 0 to u1 do b := [op(b), 1+CatalanRank(n, DeepRotateL(CatalanUnrank(n, r)))]; od; a := [op(a), CountCycles(b)]; od; RETURN(a); end;


CROSSREFS

CountCycles given in A057502, for other procedures, follow A057511 and A057501.
Similarly generated sequences: A001683, A002995, A003239, A038775, A057507. Cf. also A000081.
Occurs for first time in A073201 as row 12. Cf. A057546 and also A000081.
Sequence in context: A148072 A001430 A148073 * A006080 A287694 A148074
Adjacent sequences: A057510 A057511 A057512 * A057514 A057515 A057516


KEYWORD

nonn,more


AUTHOR

Antti Karttunen Sep 03 2000. The formula, which is absolutely impractical in the present form, added Jan 03 2003.


STATUS

approved



