|
Search: id:A115601
|
|
|
| A115601 |
|
a(n) = numerator of b(n), where b(1) = 1, b(n+1) = sum{k=1 to n} b(k)^((-1)^(n-k+1)). |
|
+0
4
|
|
| 1, 1, 2, 5, 22, 115, 1034, 10925, 197494, 4184275, 151477898, 6422862125, 465188624758, 39455642033875, 5715772632401546, 969622402982478125, 12214606115442103802, 4144208307842893353125, 2401477064538725702199814
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Sequence of numerators does not match sequence of denominators.
|
|
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).
|
|
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.
|
|
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
|
|
CROSSREFS
|
Cf. A115587, A115600, A115602.
Sequence in context: A101206 A041807 A115602 this_sequence A015557 A066305 A020093
Adjacent sequences: A115598 A115599 A115600 this_sequence A115602 A115603 A115604
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
Leroy Quet (qq-quet(AT)mindspring.com), Mar 13 2006
|
|
EXTENSIONS
|
More terms from Ryan Propper (rpropper(AT)stanford.edu), Jan 21 2007
|
|
|
Search completed in 0.002 seconds
|
