A095240 Variant of A095236, where first two people choose payphones at the ends.

1, 2, 2, 4, 4, 16, 32, 48, 96, 384, 3072, 9216, 36864, 46080, 184320, 483840, 3870720, 7741440, 82575360, 743178240, 23781703680, 59454259200, 475634073600, 2497078886400, 39953262182400, 22473709977600, 85614133248000

Offset: 1

Author

Matthew Vandermast, Jul 03 2004

Keywords

• nonn

Comments

A non-monotonic sequence: a(25) > a(26).

a(n) > a(n+1) for n = 25, 33, 49, 57, 65, 81, 97, 98, 113, 129, 130, 131, 145, 161, 162, 177, 193, 194, 195, 197, ... - Max Alekseyev, Mar 14 2019

Examples

			For example, in a 6-pay-phone situation, person A must pick either pay-phone 1 or pay-phone 6.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..100
• Simon Wundling, About a combinatorial problem with n seats and n people, arXiv:2303.18175 [math.CO], 2023. (German)

Crossrefs

Cf. A095236, A095239.

Formula

For n>1, a(n) = A095239(n-1)/(n-1) * 2. - Max Alekseyev, Mar 14 2019

For n>1, a(n) = 2 * Product_{j=1..n-1} 2^(d(n,j)) * (d(n,j))! * (b(n,j) - d(n,j))! (See A095236 for definition and calculation of b(n,j) and d(n,j)). - Simon Wundling, May 21 2023

Extensions

Edited by Max Alekseyev, Mar 14 2019