A115600 a(n) = numerator of b(n), where b(1) = 1, b(n+1) = Sum_{k=1..n} b(k)^((-1)^(n-k)).

1, 1, 2, 4, 13, 43, 905, 15790, 92494147, 47283340087, 8845558976879378539, 2707131569835749037213946965347, 2980435288285565929467276114849756995199455683357

Offset

1,3

Comments

Next term has 80 digits and is too long to be shown. - Emeric Deutsch, Apr 30 2006

Links

Michael De Vlieger, Table of n, a(n) for n = 1..19

Example

{b(n)} begins 1, 1, 2, 4, 13/2, 43/4, ...
So b(7) = 1 + 1 + 1/2 + 4 + 2/13 + 43/4 = 905/52 and therefore a(7) = 905.

Maple

b[1]:=1: for n from 1 to 14 do b[n+1]:=sum(b[k]^((-1)^(n-k)), k=1..n) od: seq(numer(b[n]), n=1..14); # Emeric Deutsch, Apr 30 2006

Mathematica

b[n_] := b[n] = If[n == 1, 1, Sum[b[k]^((-1)^(n - k - 1)), {k, n - 1}]]; Array[Numerator@ b@ # &, 13] (* Michael De Vlieger, Sep 30 2017 *)

Crossrefs

Cf. A115587, A115601, A115602.

Sequence in context: A135501 A001548 A193057 * A007858 A337797 A300931

Adjacent sequences: A115597 A115598 A115599 * A115601 A115602 A115603

Keyword

frac,nonn

Author

Leroy Quet, Mar 13 2006

Extensions

More terms from Emeric Deutsch, Apr 30 2006

Status

approved