

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
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OFFSET

0,2


COMMENTS

Numerators in the expansion of log((1x)/(12x)) / (1x) 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


LINKS

Table of n, a(n) for n=0..21.
R. J. Mathar, Notes on an attempt to prove that A097344 and A097345 are identical


MATHEMATICA

Table[ Sum[(2^(k+1)1)/(k+1), {k, 0, n}] // Numerator, {n, 0, 21}] (* JeanFrançois Alcover, Oct 14 2013, after Pari *)


PROG

(PARI) A097345(n) = numerator(sum(k=0, n, (2^(k+1)1)/(k+1)))


CROSSREFS

Cf. A097344, A134652.
Sequence in context: A264750 A205172 A139856 * A097344 A153076 A034700
Adjacent sequences: A097342 A097343 A097344 * A097346 A097347 A097348


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



