detective work needed

[N. J. A. Sloane]

A correspondent, "Thomas Sundquist" <thomas.sundquist at normandale.edu>
write to point out that A062122 does not match its description,
which is:

%I A062122
%S A062122 1,2,5,19,65,259,1161,5927,33946,216090,1513051,11558614,95658445,
%T A062122 852571616,8141450460,82928132445,897492637757,10284508144797,
%U A062122 124399102620413,1583898570128380
%N A062122 Boustrophedon transform of Fibonacci numbers (A000045).
%H A062122 J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the
 Boustrophedon on transform, J. Combin. Theory, 17A 44-54 1996 (<a href="http://www.rese
arch.att.com/~njas/doc/bous.txt">Abstract</a>, <a href="http://www.research.att
%H A062122 <a href="http://www.research.att.com/~njas/sequences/Sindx_Bo.html#boustrophe
don">Index entries for sequences related to boustrophedon transform</a>
%F A062122 a_n = Sum_{k=0..n} C(n,k) F_k E_{n-k}, where F_{k+1} = F_k + F_{k-1}, F_0 = F
_1 = 1 (A000045) and the E_k are as in A000111.
%e A062122 a_0 = F_0 = 1, a_1 = F_0 + F_1 = 2, a_2 = F_2 + a_1 + F_1 = 5, ...
%Y A062122 Sequence in context: A072468 A062666 A047116 this_sequence A047022 A014273 A0
58131
%Y A062122 Adjacent sequences: A062119 A062120 A062121 this_sequence A062123 A062124 A06
2125
%K A062122 nonn
%O A062122 0,2
%A A062122 Orleo Marinaro (KDNM21(AT)bipop.it), Jun 01 2001


The %F line does indeed define a Boustrophedon transform
of the Fibonacci numbers 1,1,2,3,5,8,13,...

The trouble is it does not give 1,2,5,19,65,259,1161,...

Rather than just say this is wrong, I would like to find
out how it really is defined.  I tried a few things without success,
and suggested to Thomas Sundquist that he write to the author.

But in the mean time, it makes a nice puzzle.  Here we have 20 terms
and some hints.  What is the sequence?  I would like to know
the answer!

Neil