login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282190 E.g.f.: 1/(1 + LambertW(1-exp(x))), where LambertW() is the Lambert W-function. 1
1, 1, 5, 40, 447, 6421, 112726, 2338799, 55990213, 1519122598, 46066158817, 1543974969769, 56677405835276, 2261488166321697, 97455090037460785, 4510770674565054000, 223183550978156866507, 11755122645815049275521, 656670295411196201190366, 38779502115371642484125915, 2413908564514961126280655257 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Stirling transform of A000312.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..375

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

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

Eric Weisstein's MathWorld, Stirling Transform

FORMULA

a(0) = 1, a(n) = Sum_{k=1..n} Stirling2(n,k)*k^k.

a(n) ~ n^n / (sqrt(1+exp(1)) * (log(1+exp(-1)))^(n+1/2) * exp(n)). - Vaclav Kotesovec, Feb 17 2017

EXAMPLE

E.g.f.: A(x) = 1 + x/1! + 5*x^2/2! + 40*x^3/3! + 447*x^4/4! + 6421*x^5/5! + 112726*x^6/6! + ...

MATHEMATICA

Range[0, 20]! CoefficientList[Series[1/(1 + ProductLog[1 - Exp[x]]), {x, 0, 20}], x]

Join[{1}, Table[Sum[StirlingS2[n, k] k^k, {k, 1, n}], {n, 1, 20}]]

PROG

(PARI) x='x+O('x^50); Vec(serlaplace(1/(1 + lambertw(1-exp(x))))) \\ G. C. Greubel, Nov 12 2017

CROSSREFS

Cf. A000312, A038052, A048802.

Sequence in context: A034000 A000359 A121886 * A052868 A292405 A094574

Adjacent sequences:  A282187 A282188 A282189 * A282191 A282192 A282193

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 08 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 21 12:10 EST 2018. Contains 299411 sequences. (Running on oeis4.)