

A091736


Numerators of the coefficients of a power series for the canonical halfexponential function.


2



1, 1, 1, 1, 1, 25, 7, 11, 5, 4001, 107, 6721, 187, 2048761, 44143, 3951137, 43663, 2300524417, 2591885, 107137061, 5512427, 4571262603161, 81607991, 10073849103649, 136193843
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OFFSET

0,6


COMMENTS

I feel that this is an important sequence, but its definition is not clear to me. As an interim measure, the link gives some additional comments that the author sent me.  N. J. A. Sloane, Jun 29 2008


LINKS

Table of n, a(n) for n=0..24.
Enrico T. Federighi, Notes on this sequence
Mathoverflow, Does the exponential function have a square root?
Mathoverflow, f(f(x))=exp(x)1 and other...


FORMULA

Starting with (1x+x^2x^3x^4), if x=sqrt(log(1.1)), this series would solve for f(1/2)= .7640669761635259978040594 ... where 1.1^f(x)=f(x+1) and f(1)=0.
Since the ratio of the absolute value of terms approaches sqrt(2.718281828...) the series converges whenever x<1/sqrt(2.718281828...).


CROSSREFS

Cf. A091737.
Sequence in context: A248139 A224807 A040606 * A245631 A243092 A126837
Adjacent sequences: A091733 A091734 A091735 * A091737 A091738 A091739


KEYWORD

sign,frac,uned,obsc


AUTHOR

Enrico T. Federighi (rico125162(AT)aol.com), Feb 02 2004


STATUS

approved



