read `ParkingStatistics.txt`:


K:=10:

print(`Explicit (Efficient!) Exact Expressions for the Factorial Moments of the AREA of a-Parking Functions up to the`, K, `-th moment`):
print(`in terms of the length(n),a,  and the Expectation`):
print(``):

print(`Definition: An  a-parking function of length n is a permutation of a weakly increasing sequence of positive integers`):
print(`x[1], ..., x[n]`):
print(`such that for all i `):
print(` x[i]<=a+i-1 `):
print(``):
print(`For any a-parking function, p, let X[p] be its AREA `):
print(``):
print(`Let E be the expectation. In this article we will present  explicit expression in terms of E,n, and a, for all factorial moments up to the `, K, `-th `):

for k from 2 to K do
gu:=collect(FactorialMomentGeneralArea(a,k,E,n),E);

print(`Theorem Number`, k, `:  the `, k, `-th factorial moment of X is`):
print(``):
print(gu):
print(``):
print(`and in Maple format`):
print(``):
lprint(gu):
print(``):
print(`and in latex`):
print(``):
print(latex(gu)):
print(``):

od:

print(`---------------------------`):
print(`This ends this article, that took`, time(), `seconds to generate. `):

quit: