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.

1, 1, 3, 42, 2730, 755160, 843461640, 3721953186000, 64522032005970000, 4400002888500992572800, 1184554667948242228538947200, 1263619612199094216947484552748800, 5357410939746060240822926481246122208000, 90477812208005548852349274940506622215042432000, 6096020095461582468665233529742777376538325820229760000

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..58 [Terms 0 through 25 were computed by G. C. Greubel]

Formula

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

a(n) = (2^n-1)!/(2^n-n)!. - N. J. A. Sloane, Feb 21 2009

Maple

a:= n-> (t-> mul(j, j=t-n+1..t-1))(2^n):
seq(a(n), n=0..15);  # Alois P. Heinz, Jan 30 2016

Mathematica

Table[(2^n - 1)!/(2^n - n)!, {n, 0, 20}] (* G. C. Greubel, Jan 30 2016 *)

Crossrefs

Sequence in context: A156108 A210929 A083402 * A213956 A157552 A058808

Adjacent sequences: A145981 A145982 A145983 * A145985 A145986 A145987

Keyword

easy,nonn

Author

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

Extensions

More terms from N. J. A. Sloane, Feb 21 2009

Status

approved