A115601 a(n) = numerator of b(n), where b(1) = 1, b(n+1) = Sum_{k=1..n} b(k)^((-1)^(n-k+1)).

1, 1, 2, 5, 22, 115, 1034, 10925, 197494, 4184275, 151477898, 6422862125, 465188624758, 39455642033875, 5715772632401546, 969622402982478125, 12214606115442103802, 4144208307842893353125, 2401477064538725702199814

Offset

1,3

Comments

Sequence of numerators does not match sequence of denominators.

The first few indices n at which A115601(n) != A115602(n+1) are 16, 29, and 38. - Jon E. Schoenfield, Nov 19 2018

Links

Michael De Vlieger, Table of n, a(n) for n = 1..116

Formula

a(n) = c(n-1)/gcd(c(n-1), c(n-2)), where c(n) = Product_{k=1..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, 30}] (* Ryan Propper, Jan 21 2007 *)
b[n_] := b[n] = If[n == 1, 1, Sum[b[k]^((-1)^(n - k)), {k, n - 1}]]; Array[Numerator@ b@ # &, 19] (* Michael De Vlieger, Sep 30 2017 *)

Crossrefs

Cf. A115587, A115600, A115602 (denominators).

Sequence in context: A228711 A215096 A115602 * A015557 A066305 A020093

Adjacent sequences: A115598 A115599 A115600 * A115602 A115603 A115604

Keyword

frac,nonn

Author

Leroy Quet, Mar 13 2006

Extensions

More terms from Ryan Propper, Jan 21 2007

Status

approved