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A091736
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Numerators of the coefficients of a power series for the canonical half-exponential function.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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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.
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LINKS
| 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...
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FORMULA
| Starting with (1-x+x^2-x^3-x^4) If x=sqrt(ln(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...).
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CROSSREFS
| Cf. A091737.
Sequence in context: A040609 A040607 A040606 * A126837 A080203 A040605
Adjacent sequences: A091733 A091734 A091735 * A091737 A091738 A091739
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KEYWORD
| sign,frac,uned,obsc
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AUTHOR
| Enrico T. Federighi (rico125162(AT)aol.com), Feb 02 2004
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