OFFSET
0,3
COMMENTS
a(10) has 40403562 decimal digits.
LINKS
Eric Weisstein's World of Mathematics, Power Tower
Wikipedia, Exponentiation
Wikipedia, Identity element
Wikipedia, Operator associativity
Wikipedia, Partition (number theory)
EXAMPLE
a(0) = 1 because the empty partition () has no parts, the exponentiation operator ^ is right-associative, and 1 is the right identity of exponentiation.
a(6) = 1^1^1^1^1^1 + 1^1^1^1^2 + 1^1^2^2 + 2^2^2 + 1^1^1^3 + 1^2^3 + 3^3 + 1^1^4 + 2^4 + 1^5 + 6 = 1 + 1 + 1 + 16 + 1 + 1 + 27 + 1 + 16 + 1 + 6 = 72.
MAPLE
f:= l-> `if`(l=[], 1, l[1]^f(subsop(1=(), l))):
a:= n-> add(f(sort(l, `<`)), l=combinat[partition](n)):
seq(a(n), n=0..9);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 15 2019
STATUS
approved