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!)
A340863 a(n) = n!*LaguerreL(n, -n^2). 2
1, 2, 34, 1626, 151064, 23046370, 5228520912, 1651548277946, 692979602529664, 372856154213080674, 250277853396112428800, 205025892171407329263802, 201314381459222197472984064, 233396220344077025321595074306 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..214

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Wikipedia, Laguerre polynomials

Index entries for sequences related to Laguerre polynomials

FORMULA

a(n) = Sum_{k=0..n} n^(2*k) * (n-k)! * binomial(n,k)^2.

a(n) = n! * [x^n] exp(n^2 * x/(1-x))/(1-x).

a(n) = A289192(n,n^2).

a(n) ~ exp(1) * n^(2*n). - Vaclav Kotesovec, Feb 14 2021

MATHEMATICA

Table[n! * LaguerreL[n, -n^2], {n, 0, 13}] (* Amiram Eldar, Feb 05 2021 *)

PROG

(PARI) a(n) = sum(k=0, n, n^(2*k)*(n-k)!*binomial(n, k)^2);

(PARI) a(n) = n!*pollaguerre(n, 0, -n^2); \\ Michel Marcus, Feb 05 2021

CROSSREFS

Main diagonal of A338435.

Cf. A277373, A289192.

Sequence in context: A215957 A171732 A291903 * A198977 A198718 A198909

Adjacent sequences:  A340860 A340861 A340862 * A340864 A340865 A340866

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 05 2021

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 June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)