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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A082545 a(n) = (2*n)! * Sum_{k=0..n} binomial(n,k)/(n+k)!. 3
1, 3, 21, 229, 3393, 63591, 1442173, 38398641, 1174226049, 40558249963, 1561734494661, 66335687785533, 3081211226192641, 155369391396527439, 8452596370942940973, 493494408990278911561, 30777323181433121541633, 2042075395611656190239571 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = n!*LaguerreL(n, n, -1).

a(n)*n+(n^3-5*n^2-n+2)*a(n-1)-2*(n+1)*(2*n-3)*(n-1)^2*a(n-2) = 0. - Vladeta Jovovic, Jul 16 2004

E.g.f.: exp((-2*x+1-(1-4*x)^(1/2))/(2*x))/(1-4*x)^(1/2). - Mark van Hoeij, Oct 31 2011

a(n) ~ n^n*2^(2*n+1/2)/exp(n-1). - Vaclav Kotesovec, Sep 27 2012

a(n) = n!*binomial(2*n,n)*hypergeom([-n], [1+n], -1). Peter Luschny, May 04 2017

a(n) = n! * [x^n] exp(x/(1 - x))/(1 - x)^(n+1). - Ilya Gutkovskiy, Nov 21 2017

MAPLE

a:= n-> simplify(n!*LaguerreL(n$2, -1)):

seq(a(n), n=0..20);  # Alois P. Heinz, Jul 27 2017

MATHEMATICA

Table[n! LaguerreL[n, n, -1], {n, 0, 17}] (* Jean-Fran├žois Alcover, Jun 04 2019 *)

CROSSREFS

Cf. A006902.

Sequence in context: A267657 A303057 A113663 * A074638 A097329 A119097

Adjacent sequences:  A082542 A082543 A082544 * A082546 A082547 A082548

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, May 11 2003

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 November 18 17:33 EST 2019. Contains 329287 sequences. (Running on oeis4.)