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Search: id:A057513
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| A057513 |
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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[n-1]+1-th and A014138[n]th terms. |
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13
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| 1, 1, 2, 4, 9, 21, 56, 153, 451, 1357, 4212, 13308, 42898, 140276, 465324, 1561955, 5300285, 18156813, 62732842, 218405402, 765657940
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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It is much faster to compute this sequence empirically with the given C-program than to calculate the terms with the formula in its present form.
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LINKS
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A. Karttunen, Gatomorphisms (with the complete Scheme source)
Index entries for sequences related to rooted trees
A. Karttunen, C-program for computing empirically the initial terms of this sequence
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FORMULA
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a(0)=1, a(n) = (1/A003418(n-1))*Sum_{i=1..A003418(n-1)} A079216(n, i) [Needs improvement.]
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MAPLE
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A057513 := proc(n) local i; `if`((0=n), 1, (1/A003418(n-1))*add(A079216bi(n, i), i=1..A003418(n-1))); 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 u-1 do b := [op(b), 1+CatalanRank(n, DeepRotateL(CatalanUnrank(n, r)))]; od; a := [op(a), CountCycles(b)]; od; RETURN(a); end;
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CROSSREFS
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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 this_sequence A006080 A148074 A130866
Adjacent sequences: A057510 A057511 A057512 this_sequence A057514 A057515 A057516
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KEYWORD
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nonn,more
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AUTHOR
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Antti Karttunen (my_firstname.my_surname(AT)iki.fi) Sep 03 2000. The formula, which is absolutely impractical in the present form, added Jan 03 2003.
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