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A115600
a(n) = numerator of b(n), where b(1) = 1, b(n+1) = Sum_{k=1..n} b(k)^((-1)^(n-k)).
4
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
KEYWORD
frac,nonn
AUTHOR
Leroy Quet, Mar 13 2006
EXTENSIONS
More terms from Emeric Deutsch, Apr 30 2006
STATUS
approved