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Search: id:A132862
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| A132862 |
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Number of permutations divided by the number of heaps on n elements. |
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+0
3
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| 1, 1, 2, 3, 8, 15, 36, 63, 192, 405, 1080, 2079, 6048, 12285, 31752, 59535, 193536, 433755, 1224720, 2488563, 7620480, 16253055, 44008272, 86266215, 274337280, 602791875, 1671742800, 3341878155, 10081895040, 21210236775, 56710659600
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) is an integer multiple of n for all n>=1.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(0)=1; a(1)=1; a(n)=n*a(nl)*a(n-1-nl) with nl=min(b-1,n-b/2) and b=2^floor(log[2](n))
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EXAMPLE
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a(4)=8 because 8=24/3 and there are 24 permutations on 4 elements, 3 of which are heaps, namely (1,2,3,4), (1,2,4,3), and (1,3,2,4). In every (min-) heap, the element at position i has to be larger than an element at position floor(i/2) for all i=1..n.
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MAPLE
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a := proc (n) option remember; local b, nl; if n<=1 then RETURN (1) fi; b:=2^trunc(simplify(log[2](n))); nl := min (b-1, n-b/2); RETURN (n*a(nl)*a(n-1-nl)); end; seq(a(i), i=0..50);
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CROSSREFS
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Cf. A000142, A056971.
Sequence in context: A128022 A011946 A080206 this_sequence A055543 A049957 A151255
Adjacent sequences: A132859 A132860 A132861 this_sequence A132863 A132864 A132865
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 18 2007
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