here,
for first series, coefficient of x^n

t_n+1 = ^rC_n

i.e. t_n+1 =  [r(r-1)(r-2) .... (r-n+1)] / n! (coefficient)

now, (1/1-x)^r
=> (1-x)^-r
 
  The binomial expansion becomes,
  => 1+(-r)(-x) + [(-r-1)(-x)²]/2! + .....

Thus, coeffecient of xⁿ is

=> t_n+1 = [r(r-1)(r-2) .... (r-n+1)] / n! (coefficient)

Thus in both cases the coefficients are the same ..