

A156972


Number of universes with n entities, exactly one being the empty set, which satisfy the Axiom of Extensionality (two sets are identical when they have the same elements) and are closed under taking subsets.


0



1, 2, 6, 60, 840, 18720, 559440, 22196160, 1092631680, 65768371200, 4703596128000, 393785778355200
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OFFSET

1,2


COMMENTS

These universes need not satisfy the Power Set Axiom.


LINKS

Table of n, a(n) for n=1..12.


EXAMPLE

1 entity = 1 universe that consists of the empty set. 2 entities = 2 universes: when a = {{}}, when a = {a} on the other hand. 3 entities = 6 universes: a = {{}}, b = {a}; a = {{}}, b = {b}; and so on. 4 entities = 60 universes...


CROSSREFS

Cf. A145984
Sequence in context: A056604 A215720 A211936 * A086332 A180402 A338600
Adjacent sequences: A156969 A156970 A156971 * A156973 A156974 A156975


KEYWORD

hard,nonn,nice,more


AUTHOR

Csabay Karoly (csabay58(AT)gmail.com), Feb 19 2009, Jun 14 2009, Mar 20 2010


STATUS

approved



