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A097345
Numerators of the partial sums of the binomial transform of 1/(n+1).
4
1, 5, 29, 103, 887, 1517, 18239, 63253, 332839, 118127, 2331085, 4222975, 100309579, 184649263, 1710440723, 6372905521, 202804884977, 381240382217, 13667257415003, 25872280345103, 49119954154463, 93501887462903
OFFSET
0,2
COMMENTS
Numerators in the expansion of log((1-x)/(1-2x)) / (1-x) are 0,1,5,29,.. - Paul Barry, Feb 09 2005
Is this identical to A097344? - Aaron Gulliver, Jul 19 2007. The answer turns out to be No - see A134652.
From n=9 on, the putative formula a(n)=A003418(n+1)*sum{k=0..n, (2^(k+1)-1)/(k+1)} is false. The least n for which a(n) is different from A097344(n) is n=59, then they agree again until n=1519. - M. F. Hasler, Jan 25 2008
MATHEMATICA
Table[ Sum[(2^(k+1)-1)/(k+1), {k, 0, n}] // Numerator, {n, 0, 21}] (* Jean-François Alcover, Oct 14 2013, after Pari *)
PROG
(PARI) A097345(n) = numerator(sum(k=0, n, (2^(k+1)-1)/(k+1)))
CROSSREFS
Sequence in context: A264750 A205172 A139856 * A097344 A153076 A034700
KEYWORD
easy,nonn,frac
AUTHOR
Paul Barry, Aug 06 2004
EXTENSIONS
Edited and corrected by Daniel Glasscock (glasscock(AT)rice.edu), Jan 04 2008 and M. F. Hasler, Jan 25 2008
Moved comment concerning numerators of the logarithm from A097344 to here where it is correct - R. J. Mathar, Mar 04 2010
STATUS
approved