login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A305276 Expansion of e.g.f. 1/(1 + LambertW(-x/(1 - x))). 3
1, 1, 6, 57, 748, 12565, 257526, 6232765, 173980920, 5502613833, 194477548330, 7596028355641, 324920533473108, 15106155118606045, 758463525318426942, 40901033617318501845, 2357682497456804486896, 144670077586483815863569, 9414952083720893890165842, 647715776085173413399687633 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Lah transform of A000312.

LINKS

Robert Israel, Table of n, a(n) for n = 0..369

N. J. A. Sloane, Transforms

FORMULA

a(n) = Sum_{k=0..n} binomial(n-1,k-1)*k^k*n!/k!.

a(n) ~ n^n * (1 + exp(1))^(n - 1/2) / exp(n - 1/2). - Vaclav Kotesovec, Aug 18 2018

MAPLE

S:= series(1/(1+LambertW(-x/(1-x))), x, 51):

seq(coeff(S, x, j)*j!, j=0..50); # Robert Israel, Aug 19 2018

MATHEMATICA

nmax = 19; CoefficientList[Series[1/(1 + LambertW[-x/(1 - x)]), {x, 0, nmax}], x] Range[0, nmax]!

Join[{1}, Table[Sum[Binomial[n - 1, k - 1] k^k n!/k!, {k, n}], {n, 19}]]

CROSSREFS

Cf. A000312, A052871, A060356, A305304.

Sequence in context: A107718 A308863 A000406 * A032119 A294511 A242817

Adjacent sequences:  A305273 A305274 A305275 * A305277 A305278 A305279

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 18 2018

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 10 22:22 EDT 2020. Contains 336403 sequences. (Running on oeis4.)