OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..365
FORMULA
a(n) = n!*LaguerreL(n, n, -1).
n*a(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-François Alcover, Jun 04 2019 *)
PROG
(PARI) a(n) = sum(k=0, n, k!*binomial(n, k)*binomial(2*n, k)); \\ Seiichi Manyama, May 01 2021
(PARI) a(n) = n!*pollaguerre(n, n, -1); \\ Seiichi Manyama, May 01 2021
(Magma) [Factorial(n)*Evaluate(LaguerrePolynomial(n, n), -1): n in [0..40]]; // G. C. Greubel, Aug 11 2022
(SageMath) [factorial(n)*gen_laguerre(n, n, -1) for n in (0..40)] # G. C. Greubel, Aug 11 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, May 11 2003
STATUS
approved