OFFSET
0,2
COMMENTS
For m > 4, (-1)^n * n! * Laguerre(n, m*n) ~ sqrt(1/2 + (m-2)/(2*sqrt(m*(m-4)))) * exp((m - 2 - sqrt(m*(m-4)))*n/2) * ((m - 2 + sqrt(m*(m-4)))/2)^n * n^n.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..310
FORMULA
a(n) ~ sqrt(1/2 + 1/sqrt(3)) * 2^n * exp((2-sqrt(3))*n) * ((1 + sqrt(3))/2)^(2*n) * n^n.
MATHEMATICA
Table[(-1)^n * n! * LaguerreL[n, 6*n], {n, 0, 20}]
Flatten[{1, Table[n!*Sum[Binomial[n, k] * (-1)^(n-k) * 6^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]
Table[(-1)^n * n! * Hypergeometric1F1[-n, 1, 6*n], {n, 0, 20}]
PROG
(PARI) a(n) = (-1)^n*n!*pollaguerre(n, 0, 6*n); \\ Michel Marcus, Feb 05 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 20 2020
STATUS
approved