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.

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

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: A371018 A376476 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