This is With no information over we can't do much.
One "cheap" way to do this is to assume there is one specific answer, independent of x. If the answer does not depend on x, take x= 0 and immediately the sequence is 0, 0, 0, 0,...
If x is not 0, we can at least assume x> 0 since otherwise is not defined for some t. And it is well known that t! dominates any x to the t power. One way of looking at it is this: the numerator and denominator both include t factors. In the numerator, the factor is always x. In the denominator the factors are from 1 up to t so for large enough t, the denominator is larger than the numerator- and as t gets larger the difference gets greater.