nC3 = 2(nC4)

n!/3!(n-3)! = 2n!/4!(n-4)!

1/3!(n-3)! = 2/4!(n-4)!

1/3! = 1/2(3!)(n-4)

1 = 1/2(n-4)

n-4 = 1/2

n = 4.5

1

11

121

1331 3rd term is 3 times 4th term

14641 3rd term is 1.5 times 4th term

15101051 3rd term is = 4th term

1615201561 3rd term < 4th term

172145452171

1,8,28, 66, 90...

there is no integer n where the 4th term has a coefficient half the 3rd term, n=4.5 would work though

for 3/2 times the 4th term, n<3

nC3 = (3/2)nC4

n!/3!(n-3)! = 3n!/2(4!)(n-4)!

1 = 3/8(n-1)

n-1= 3/8

n = 1.375