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A092124
a(0) = 2, a(n) = (2^(2^n)+2)*a(n-1) for n>0.
4
2, 12, 216, 55728, 3652301664, 15686516209310983872, 289365149921256212111714425927549504896, 98465858119637274097902770931519409290135390781788892125023848289699334298368
OFFSET
0,1
COMMENTS
In binary representation a(n) can be interpreted as an expression to represent n according to John von Neumann's definition of natural numbers: braces are coded as 1 and 0 and the empty set as 10={};
a(n) = (A001146(n)+2)*a(n-1) = 2*(A058891(n)+1)*a(n-1).
LINKS
EXAMPLE
a(3)=55728='1101100110110000' -> {{}{{}}{{}{{}}}} -> {{},{{}},{{},{{}}}} -> {0,{0},{0,{0}}} -> {0,1,{0,1}} -> {0,1,2} -> A001477(3)=3.
MATHEMATICA
RecurrenceTable[{a[0]==2, a[n]==(2^(2^n)+2)a[n-1]}, a, {n, 8}] (* Harvey P. Dale, Nov 15 2020 *)
nxt[{n_, a_}]:={n+1, (2^2^(n+1)+2)a}; NestList[nxt, {0, 2}, 8][[;; , 2]] (* Harvey P. Dale, Aug 11 2023 *)
PROG
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A092124(n): return ((1<<(1<<n))+2)*A092124(n-1) if n else 2 # Chai Wah Wu, Nov 23 2023
CROSSREFS
Sequence in context: A208651 A083667 A374871 * A009525 A009683 A132879
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Mar 30 2004
STATUS
approved