Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A001662
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A001662 Numerators in expansion of W(exp(x)) about x=1, where W is the Lambert function.
(Formerly M4896 N2098)
+0
3
1, 1, 1, -1, -1, 13, -47, -73, 2447, -16811, -15551, 1726511, -18994849, 10979677, 2983409137, -48421103257, 135002366063, 778870772857, -232033147779359, 1305952009204319, 58740282660173759, -1862057132555380307, 16905219421196907793 (list; graph; listen)
OFFSET

0,6

COMMENT

Coefficients of Airey's converging factor.

(-1)^n times the polynomials with coefficients in triangle A008517, evaluated at -1. - Ralf Stephan, Dec 13 2004

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

J. R. Airey, The "converging factor" in asymptotic series and the calculation of Bessel, Laguerre and other function, Phil. Mag., 24 (1937), 521-552 [ gives 22 terms ].

J. C. P. Miller, A method for the determination of converging factors ..., Proc. Camb. Phil. Soc., 48 (1952), 243-254.

F. D. Murnaghan, Airey's converging factor, Proc. Nat. Acad. Sci. USA, 69 (1972), 440-441.

F. D. Murnaghan and J. W. Wrench, Jr., The Converging Factor for the Exponential Integral, Report 1535, David Taylor Model Basin, U.S. Dept. of Navy, 1963 [ gives first 67 terms ].

P. Wynn, Converging factors for the Weber parabolic cylinder functions of complex argument, Proc. Konin. Ned. Akad. Weten., Series A, 66 (1963), 721-754 (two parts).

LINKS

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.

J. M. Borwein and R. M. Corless, Emerging tools for experimental mathematics, Amer. Math. Monthly, 106 (No. 10, 1999), 889-909.

FORMULA

Let b(n) = a(n)/2^n; then the e.g.f. B(x)=Sum b(n)x^n/n! satisfies exp B(x) = 1 + 2x - B(x).

EXAMPLE

W(exp(x)) = 1 +(x-1)/2+(x-1)^2/16-(x-1)^3/192-...

MAPLE

series(LambertW(x), x=1, 45);

PROGRAM

(PARI) a(n)=if(n<1, !n, n!*4^n/2*polcoeff(serreverse(x+log(1+x+x*O(x^n))), n))

CROSSREFS

Cf. A051711.

Sequence in context: A116476 A035340 A127305 this_sequence A031390 A113943 A004467

Adjacent sequences: A001659 A001660 A001661 this_sequence A001663 A001664 A001665

KEYWORD

sign,easy,nice,frac

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 07 1999

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


AT&T Labs Research