login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A277423 a(n) = n!*LaguerreL(n, n). 15

%I #14 Sep 08 2022 08:46:17

%S 1,0,-2,6,24,-380,720,31794,-361088,-2104056,101548800,-612792290,

%T -25534891008,593660731404,2831189530624,-361541172525750,

%U 4481749181890560,169464194149739536,-6805365045197340672,-9663483091971306186,6883830206467440640000

%N a(n) = n!*LaguerreL(n, n).

%H G. C. Greubel, <a href="/A277423/b277423.txt">Table of n, a(n) for n = 0..415</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>

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

%F a(n) = n! * [x^n] exp(-n*x/(1 - x))/(1 - x). - _Ilya Gutkovskiy_, Nov 21 2017

%t Table[n!*LaguerreL[n, n], {n, 0, 20}]

%t Flatten[{1, Table[n!*Sum[Binomial[n, k] * (-1)^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]

%t Table[n! * Hypergeometric1F1[-n, 1, n], {n, 0, 20}] (* _Vaclav Kotesovec_, Feb 20 2020 *)

%o (PARI) for(n=0, 30, print1(n!*sum(k=0,n, binomial(n,k)*(-1)^k*n^k/k!), ", ")) \\ _G. C. Greubel_, May 16 2018

%o (Magma) [Factorial(n)*(&+[Binomial(n,k)*(-1)^k*n^k/Factorial(k): k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, May 16 2018

%Y Cf. A277373, A277391, A277392, A277418, A277419, A277420, A277421, A277422.

%Y Cf. A002720, A087912, A277382.

%K sign

%O 0,3

%A _Vaclav Kotesovec_, Oct 14 2016

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)