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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 (list; graph; refs; listen; history; text; internal format)
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

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}] (* Jean-Fran├žois 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

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Last modified December 12 01:08 EST 2017. Contains 295936 sequences.