#3 ANOTHER SEQUENCE


What is the next number in the following sequence?

1 - 4 - 17 - 66 - 247 - 918 - 3425


Correct answer: 12862

Explanation:

The numbers of this sequence are calculated by

binomial (2n,n) - n

where n is the number of the member.
n=1: binomial  (2,1) - 1 =  2!/(1!1!) - 1 =     2 - 1 =     1
n=2: binomial  (4,2) - 2 =  4!/(2!2!) - 2 =     6 - 2 =     4
n=3: binomial  (6,3) - 3 =  6!/(3!3!) - 3 =    20 - 3 =    17
n=4: binomial  (8,4) - 4 =  8!/(4!4!) - 4 =    70 - 4 =    66
n=5: binomial (10,5) - 5 = 10!/(5!5!) - 5 =   252 - 5 =   247
n=6: binomial (12,6) - 6 = 12!/(6!6!) - 6 =   924 - 6 =   918
n=7: binomial (14,7) - 7 = 14!/(7!7!) - 7 =  3432 - 7 =  3425
n=8: binomial (16,8) - 8 = 16!/(8!8!) - 8 = 12870 - 8 = 12862


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© Andreas Rottler


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