The OEIS is supported by the many generous donors to the OEIS Foundation.

Group the natural numbers such that the product of the n-th group is divisible by 2^n. (1), (2), (3,4), (5,6,7,8), (9,10,11,12,13,14),(15,16,17,18), ... Sequence contains the product of the terms of the groups.

3

`%I #13 Jul 30 2015 07:33:22
`

`%S 1,2,12,1680,2162160,73440,96909120,424097856000,5339572260422400,
`

`%T 57407703889536000,1573144097507348889600,89247024757574635311360000,
`

`%U 131197375012291112448000,6932022668773077815267328000
`

`%N Group the natural numbers such that the product of the n-th group is divisible by 2^n. (1), (2), (3,4), (5,6,7,8), (9,10,11,12,13,14),(15,16,17,18), ... Sequence contains the product of the terms of the groups.
`

`%F From _Chayim Lowen_, Jul 29 2015: (Start)
`

`%F Product_{m=0..n} a(m) = (A085897(n+1)-1)! whence:
`

`%F a(n) = (A085897(n+1)-1)!/a(n-1).
`

`%F a(n) = (A085897(n+1)-1)!/(A085897(n)-1)!. (End)
`

`%e a(3) = 1680 = 5*6*7*8 = 2^3*(5*6*7) is divisible by 2^3=8. (In fact, it is divisible by 2^4, but 5*6*7 is not divisible by 8.)
`

`%Y Cf. A085896, A085897, A085898.
`

`%K nonn
`

`%O 0,2
`

`%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jul 10 2003
`

`%E More terms from _Ray Chandler_, Sep 13 2003
`