A115602 a(n) = denominator of b(n), where b(1) = 1, b(n+1) = Sum_{k=1..n} b(k)^((-1)^(n-k+1)).

1, 1, 1, 2, 5, 22, 115, 1034, 10925, 197494, 4184275, 151477898, 6422862125, 465188624758, 39455642033875, 5715772632401546, 42157495781846875, 12214606115442103802, 4144208307842893353125, 2401477064538725702199814

Offset

1,4

Comments

Sequence of numerators does not match sequence of denominators.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..117

Formula

a(n) = c(n-2)/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) = 1034.

Mathematica

b = {1}; Do[AppendTo[b, Sum[b[[k]]^((-1)^(n - k + 1)), {k, 1, n}]], {n, 1, 30}]; Table[Denominator[b[[j]]], {j, 1, Length[b]}] (* Stefan Steinerberger, Oct 16 2007 *)

Crossrefs

Cf. A115587, A115600, A115601 (numerators).

Sequence in context: A041807 A228711 A215096 * A115601 A015557 A066305

Adjacent sequences: A115599 A115600 A115601 * A115603 A115604 A115605

Keyword

frac,nonn

Author

Leroy Quet, Mar 13 2006

Extensions

More terms from Stefan Steinerberger, Oct 16 2007

Status

approved