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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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1
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OFFSET
| 0,2
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COMMENTS
| 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
| 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
| Sequence in context: A122743 A137032 A053421 * A181430 A001593 A124546
Adjacent sequences: A083693 A083694 A083695 * A083697 A083698 A083699
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), May 22 2003
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