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Search: id:A056972
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| A056972 |
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Heaps on n levels (i.e. of 2^n - 1 elements). |
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2
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| 1, 1, 2, 80, 21964800, 74836825861835980800000, 2606654998899867556195703676289609067340669424836280320000000000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A sequence {a_i}_{i=1}^N forms a (binary) heap if is satisfies a_i<a_{2i} and a_i<a_{2i+1} for 1<=i<=(N-1)/2
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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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EXAMPLE
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There is 1 heap on 2^0-1=0 elements, 1 heap on 2^1-1=1 element, and there are 2 heaps on 2^2-1=3 elements, and so on.
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MAPLE
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a:=n->(2^n-1)!/product((2^k-1)^(2^(n-k)), k=1..n); seq(a(i), i=0..6); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 22 2007
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MATHEMATICA
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s[1] := 1; s[l_] := s[l] := Binomial[2^l-2, 2^(l-1)-1]s[l-1]^2; Table[s[l], {l, 10}]
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CROSSREFS
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Cf. A056971.
Sequence in context: A123828 A008563 A059487 this_sequence A051391 A041799 A072408
Adjacent sequences: A056969 A056970 A056971 this_sequence A056973 A056974 A056975
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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