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A115601
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a(n) = numerator of b(n), where b(1) = 1, b(n+1) = sum{k=1 to n} b(k)^((-1)^(n-k+1)).
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3
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1, 1, 2, 5, 22, 115, 1034, 10925, 197494, 4184275, 151477898, 6422862125, 465188624758, 39455642033875, 5715772632401546, 969622402982478125, 12214606115442103802, 4144208307842893353125, 2401477064538725702199814
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Sequence of numerators does not match sequence of denominators.
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FORMULA
| a(n) = c(n-1)/GCD(c(n-1),c(n-2)), where c(n) = product{k=1 to floor(n/2)} (3*2^(n-2k) -1).
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EXAMPLE
| {b(n)} begins 1, 1, 2, 5/2, 22/5, 115/22, 1034/115,...
So b(7) = 1 + 1 + 1/2 + 5/2 + 5/22 + 115/22 + 115/1034 = 10925/1034 and therefore a(7) = 10925.
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MATHEMATICA
| l = {1}; Do[k = Length[l]; b = Sum[l[[i]]^((-1)^(k-i+1)), {i, 1, k}]; AppendTo[l, b]; Print[Numerator[b]], {n, 1, 30}] - Ryan Propper (rpropper(AT)stanford.edu), Jan 21 2007
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CROSSREFS
| Cf. A115587, A115600, A115602.
Sequence in context: A177251 A041807 A115602 * A015557 A066305 A020093
Adjacent sequences: A115598 A115599 A115600 * A115602 A115603 A115604
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KEYWORD
| frac,nonn
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AUTHOR
| Leroy Quet Mar 13 2006
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EXTENSIONS
| More terms from Ryan Propper (rpropper(AT)stanford.edu), Jan 21 2007
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