EDITED A097344

[Maximilian Hasler]

the link to Mathar's PDF was wrong, the index of A081528 in %F was wrong,
(in A097345 the corresponding index is wong, too - I'll edit...),
but in fact the whole formula was wrong and most terms from a(9) on were wrong.
(I noticed that if the formula was true, then Mathar's notes would
have proved that A097344=A097345.)

Neil, there is also a minor typo on your "hot sequences" page :
correct "primes factors" => "prime factors".
(Now you'll have to rewrite that page, anyway...)
Maximilian

%I A097344
%S A097344 1, 5, 29, 103, 887, 1517, 18239, 63253, 332839, 118127,
2331085, 4222975, 100309579, 184649263,
%T A097344 1710440723, 6372905521, 202804884977, 381240382217,
13667257415003, 25872280345103,
%U A097344  49119954154463, 93501887462903, 4103348710010689,
7846225754967739, 75162749477272151
%N A097344 Numerators in binomial transform of 1/(n+1)^2.
%C A097344 Numerators in the expansion of ln((1-x)/(1-2x))/(1-x) are
0,1,5,29,.. - Paul Barry
               (pbarry(AT)wit.ie), Feb 09 2005
%C A097344 Is this identical to A097345? - Aaron Gulliver, Jul 19 2007
%C A097344 If the formula a(n)=A081528(n) sum{k=0..n, binomial(n,
k)/(k+1)^2} were true, then A097344 = A097345 according to Mathar's
notes. However, the term n=9 in the binomial transform of 1/(n+1)^2
has the denominator 5040=A081528(9)/4=A081528(10)/5. - M. Hasler, Jan
25 2008
%H A097344 R. J. Mathar, <a
href="http://www.research.att.com/~njas/sequences/a097345.pdf">
               Notes on an attempt to prove that A097344 and A097345
are identical</a>
%o A097344 (PARI)
A097344(n)=numerator(sum(k=0,n,binomial(n,k)/(k+1)^2)) \\ - M. Hasler,
Jan 25 2008
%Y A097344 Adjacent sequences: A097341 A097342 A097343 this_sequence
A097345 A097346 A097347
%Y A097344 Sequence in context: A087348 A050409 A111937 this_sequence
A097345 A034700 A057721
%K A097344 easy,nonn,frac
%O A097344 0,2
%A A097344 Paul Barry (pbarry(AT)wit.ie), Aug 06 2004
%E A097344 Edited and corrected by Maximilian F. Hasler
(Maximilian.Hasler(AT)gmail.com), Jan 25 2008