

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



1, 1, 3, 42, 2730, 755160, 843461640, 3721953186000, 64522032005970000, 4400002888500992572800, 1184554667948242228538947200, 1263619612199094216947484552748800, 5357410939746060240822926481246122208000, 90477812208005548852349274940506622215042432000, 6096020095461582468665233529742777376538325820229760000
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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^n1,n1).
a(n) = (2^n1)!/(2^nn)!.  N. J. A. Sloane, Feb 21 2009


MAPLE

a:= n> (t> mul(j, j=tn+1..t1))(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



