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Search: id:A083696
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| A083696 |
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a(n)=Sum[Prod(2^n-k),(k=0,2r-1)]5^r/(2r)!,(r=0,2^(n-1)). |
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+0
2
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| 1, 6, 56, 6016, 72318976, 10460064284409856, 218825889667954898996994670329856, 95769539977943941232017762100658986141884645207653888255921750016
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)/A083697(n) converges to sqrt(5). a(n)=a(n-1)^2+5*A083697(n-1)^2. Similar to A081459: a(n) is the numerator of the same mapping f(r)=(1/2)(r+5/r) but with initial value r=1.
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MATHEMATICA
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Table[Sum[Product[2^n - k, {k, 0, 2*r - 1}]k^r/(2*r)!, {r, 0, 2^(n - 1)}], {n, 0, 8}]
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CROSSREFS
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Sequence in context: A122743 A137032 A053421 this_sequence A001593 A124546 A144070
Adjacent sequences: A083693 A083694 A083695 this_sequence A083697 A083698 A083699
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), May 22 2003
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