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 A145984 Number of "universes" built from n entities according to the following rules: 1. Each of the entities can be an element or a set. 2. Sets are entities that do have another entity as an element. 3. There must exist an element. 4. Two sets are identical when they own the same elements. 2

%I

%S 1,1,3,42,2730,755160,843461640,3721953186000,64522032005970000,

%T 4400002888500992572800,1184554667948242228538947200,

%U 1263619612199094216947484552748800,5357410939746060240822926481246122208000,90477812208005548852349274940506622215042432000,6096020095461582468665233529742777376538325820229760000

%N Number of "universes" built from n entities according to the following rules: 1. Each of the entities can be an element or a set. 2. Sets are entities that do have another entity as an element. 3. There must exist an element. 4. Two sets are identical when they own the same elements.

%H Alois P. Heinz, <a href="/A145984/b145984.txt">Table of n, a(n) for n = 0..58</a> [Terms 0 through 25 were computed by G. C. Greubel]

%F a(n) = variations(2^n-1,n-1).

%F a(n) = (2^n-1)!/(2^n-n)!. - _N. J. A. Sloane_, Feb 21 2009

%p a:= n-> (t-> mul(j, j=t-n+1..t-1))(2^n):

%p seq(a(n), n=0..15); # _Alois P. Heinz_, Jan 30 2016

%t Table[(2^n - 1)!/(2^n - n)!, {n, 0, 20}] (* _G. C. Greubel_, Jan 30 2016 *)

%K easy,nonn

%O 0,3

%A Csabay Karoly (csabay58(AT)gmail.com), Oct 26 2008; entry revised Feb 19 2009, Apr 21 2010

%E More terms from _N. J. A. Sloane_, Feb 21 2009

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Last modified September 25 23:58 EDT 2021. Contains 347664 sequences. (Running on oeis4.)