OFFSET
0,3
FORMULA
a(n) = n!*LaguerreL(n, -n) - n^n.
a(n) = (-1)^n*KummerU(-n, 1, -n) - n^n.
a(n) = n^n*(hypergeom([-n, -n], [], 1/n) - 1) for n>=1.
a(n) ~ n^n * phi^(2*n+1) * exp(n/phi-n) / 5^(1/4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Oct 12 2016
MAPLE
PROG
(PARI) a(n) = sum(k=1, n, binomial(n, n-k)*n^(n-k)*n!/(n-k)!); \\ Michel Marcus, Oct 12 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Oct 11 2016
STATUS
approved