A091736 Numerators of the coefficients of a power series for the canonical half-exponential function.

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

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 (1-x+x^2-x^3-x^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